Import of Gold by NRIs

Yes , they can bring gold to India though Reserve Bank of India has granted general permission to persons of Indian nationality or origin to bring into India a limited amount of gold and silver. However, import of gold and silver is govern by certain rules and regulation and are given in detail below.

A NRI who has been residing in a foreign country for over one year and is returning to India may be allowed to import jewellery without paying any custom duty in his use up to an aggregate value of ten thousand rupees in the case of a male passenger. In case of a female passenger, an individual can import gold of up to rupees twenty thousands.
If the amount of gold imported exceeds the import duty free range, then the custom duty charges an amount of Rs. 250 per 10 gms of gold. Even in such a situation, an individual is only permitted to import a maximum of 10 kg of Gold as a part of their baggage after paying the required customs duty. It should also be noted that that these facilities is given only to those passengers who is coming to India after a stay abroad of about six months.
Gold may be brought into India in any form, including ornaments; however, a declaration is needed to be filled by the importer for obtaining the permitted quantity of gold from customs bonded warehouse of State Bank of India or from Metal & Mineral Trading Corporation subject to other conditions.
In case where a passenger has declared the gold, but could not clear it for want of sufficient foreign exchange for paying Customs duty, then re-export of the same may be permitted.

please refer Baggage (Amendment) Rules, 2006.