Investment by NRI's/OCB's in Indian mutual funds is allowed.
The amount is invested out of NRE/FCNR/NRO account.

For details of mutual funds click here

Taxation For NRI's

Investment in secondary market
NRI's can invest in secondary market through Portfolio investment in equity shares/convertible debentures.

Investment in new issues
NRI's can invest in new issues (shares/convertible debentures).

Investment in debentures
NRI's can invest in non convertible debentures.

Bank Deposit
NRI's can invest in Banks' deposits accounts out of the funds remitted from abroad or foreign exchange brought in India.