Identity-based (ID-based) encryption is a very important cryptographic primitive. It is advantageous over the conventional public key cryptosystems due to direct and easy verification of the public keys. The security of most of the ID-based encryption schemes is based directly or indirectly on solving integer factorizationproblem, Elliptic curve discrete logarithm problem or discrete logarithm problem. It is known that these well-studied problems are not safe against attacks on a sufficiently large quantum computer. Therefore, in this paper we propose a secure ID-based encryption scheme whose security depends on the newly discovered hard problems in the algebraic structure of group rings. We show that the proposed scheme is IND-ID-CPA secure and safe against the chosen ciphertext attack. Moreover, we also comment on the IND-ID-CCA security of theproposed scheme.