You can check the top marine engineering colleges below

Amity University, Noida

Vels University, Chennai

Chandigarh College of Engineering and Technology, Chandigarh

CV Raman College of Engineering, Bhubaneswar

Indian Maritime University, Chennai

To check the complete list you can also refer below link

Top Marine Engineering Colleges

In order to take admission in these colleges you have to appear for engineering entrance exam like JEE Main and you can also take admission in your state level entrance exam 

Good Luck!!