This paper presents a new public key cryptosystem that uses noncommutative groups as platform group. The underlying hard problem of the proposed cryptosystem is a combination of discrete log problem and conjugacy search problem. Due to use of noncommutative platform groups, it is expected that the presented cryptosystem provides higher levels of security against known attacks. Some important issues regarding the choice of platform and parameters of this cryptosystem are addressed. Further, a brief analysis of security aspects is also presented.