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You'll have to provide a certificate of no impediment to marry legally here, that stating there is no reason you can't be married legally.
Your only other option is a local religious wedding. That won't be questioned if you live in a village but immigration and other officials probably won't accept it.
Only having the one wife I'm unsure of the rules but I understand the imam will ask for a letter of agreement from your first wife.
Polygamy is legal here but is neither popular nor generally considered acceptable.

Dear Fred,
Thanks for your kind reply. I just want to know, this NOC (no objection certificate) from my parents and permission letter from my first wife is needed to submit in Indian embassy in Jakarta?

The no impediment letter is issued by your government. I have no real idea if it's possible from your embassy but it won't be possible if your country doesn't allow Polygamy.
If you intend to live in Indonesia, immigration likely won't accept your marriage so visas could be a problem.

Dear Fred,
In India, Muslim's can have four wives. Indian government allowed polygamy for Indian Muslims according to Muslim Personal Law Act. So, my question is, if Indian government can allow me to marry with another girl, I have to submit that record in Jakarta in Indian embassy? Onwards, I have no impediment from my parents and permission from first wife in form of notary or affidavit.

This requires confirmation as I have no experience of it, but it seems the second marriage has no legal status here so you can get married under Islamic rules but that will not be accepted as a legal marriage by  officialdom.
That needs checking at your local Indonesian embassy but my local officials say they wouldn't accept it (I asked for you this morning).

Assuming my local RW (Village head) is correct, that means no immigration status as a spouse would be possible.

Respectfully young man, why on earth would you not respect your first wife's wishes and let her be free...She is not some sort of toy or utility you can hold onto for your life ...you either love her and look after her as your wife or have the courage to leave her altogether and start fresh with your new partner...please think of others and treat woman in a way you would like to be treated yourself...

The validity of the above comments depends on a lot of factors (The first wife may not want to divorce) but the legal void mean there is no easy way for the OP to come and live here and any marriage would be a religious marriage only meaning any possible kids would also have a lot of problems in the future, especially with official documents such as a KTP or passport.
I would very strongly suggest a second marriage in this country is a bad idea for the wife and any resulting kids.
No problem for the man except he can't stay here on a spouse sponsored visa and his chances of any other long term visa are very limited.

I've been reading this website, but this is the first time I just want to post. I'm indonesian female btw.
So to answer your question. In Indonesia a muslim man can marry up to 4 wives legally. However, it is not a practice that is too common and could still be frowned upon, even among muslim.

on the legal side, if you want to married the second time, as an Indonesian, you need to provide a written consent and approval from your first wife and your bride-to-be. Even then, don't be surprise if the officer from KUA (office of Islamic religious affair/the one that gives out marriage certificate) will ask more than once if any of the party (you, first wife, bride to be) are sure about this and perhaps even ask your first wive and your bride-to-be (and her father/legal guardian) to come forward so the officer can ask them personally and make sure those written consents are not forced upon them. There will be questions about how you provide for both households, especially if your first wife is in India. How will you manage to treat both of your wives and all of your children with justice either financially, time, attention, love, etc. Please remember that even though Islam permits up to 4 wives, it's not without its consequences. "And if you fear that you will not deal justly with the orphan girls, then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those your right hand possesses. That is more suitable that you may not incline [to injustice]. (QS 4:3)"

My next question, are you coming to Indonesia just to get a second wife??? If simply marrying more than once is your goal, find your 2nd wive in your home country. Less paperwork and headache. Or find women who are less fortunate (i.e widowed-jobless- refugee with 3 or more dependents). At least people would see you as a helping guy, not a wandering d**k.

tarponjohn2002 wrote:

Respectfully young man, why on earth would you not respect your first wife's wishes and let her be free...She is not some sort of toy or utility you can hold onto for your life ...you either love her and look after her as your wife or have the courage to leave her altogether and start fresh with your new partner...please think of others and treat woman in a way you would like to be treated yourself...

Agreed! Thank you Sir...

A lot of this is down to the reasons for marriage.
If it's a visa, forget it - Won't work.

Yup it won't work is he's aiming for visa. Even if you are Indonesian, it's not easy to do polygamy legally (compare to your first marriage), let alone a foreigner.