There are several institutes in India offerring the courses in VLSi complete design flow.
You can opt from the following institutes that r supposed to be among the best in INDIA.
1) C-DAC Pune (PG Diploma in VLSI)
2) ICIT, Pune ( PG Diploma in VLSI)
3) VEDA-IIT, Hyderabad ( Post Graduation in VLSI including MS)
4) Vedant, Mohali ( PG Diploma in VLSI)
5)Sandeepani, Banglore (PG Diploma in VLSI)
othere then above i have heard of IIT, Delhi also offering the short term course in VLSI, But i am not sure about it.