Here is the following list of some Top Private Universities in India, which you are looking for

Vellore Institute of Technology University
Vellore

Birla Institute of Technology and Science
Pilani

Manipal University
Manipal

Birla Institute of Technology
Mesra

Amrita Vishwa Vidyapeetham University
Coimbatore

SASTRA University
Thanjavur

Bharati Vidyapeeth
Pune

SRM University
Chennai

Thapar University
Patiala

Amity University
Noida

Sri Ramachandra University
Chennai

International Institute of Information Technology
Hyderabad

ICFAI Foundation for Higher Education
Hyderabad

Nirma University
Ahmedabad

TERI University
New Delhi

Kalinga Institute of Industrial Technology
Bhubhaneswar

Karunya University
Coimbatore

Bharath University
Chennai

Gandhi Institute of Technology and Management
Vishakhapatnam

Manav Rachna International University
Faridabad

Padmashree Dr DY Patil Vidyapeeth
Navi Mumbai

NITTE University
Mangalore

Banasthali University
Banasthali

Sri Sathya Sai Institute of Higher Learning
Anantapur

Vel Tech Dr RR and Dr SR Technical University
Chennai

University of Petroleum and Energy Studies
Dehradun

Dhirubhai Ambani Institute of Information and Communication Technology
Gandhinagar

Avinashilingam Institute for Home Science and Higher Education for Women University
Coimbatore

JSS University
Mysore

KLE University
Belgaum