All NRIs/PIOs (Person Of Indian Origin) are allowed to invest in Indian Stock Market through a special purpose vehicle proposed by the Reserve Bank Of India (RBI) called Portfolio Investment Scheme (PIS). Like a normal Indian investor the NRI also needs to have a Trading Account and Demat Account. But for banking activities he has to have a separate PIS account. To have these three types of account an NRI needs the following -
1- Designated Bank to facilitate opening of PIS Account
2- Trading Member/Broker to provide a Trading Account
3- Depository Participant to provide a Demat Account

Please check with ICICI Direct, Share Khan they provide these accounts.