Group Encryption (GE) is a recently proposed cryptographic primitive protecting the privacy of the receivers in a communication system. A majority of group encryption schemes are implicitly based on public key infrastructure (PKI) setting in which the management of certificates are complicated. Identity based encryption (IBE) seems to be a good alternative for PKI in GE, but the private key escrow and the user revocation problem are inherent in IBE system. Certificate-based encryption (CBE) overcomes drawbacks of PKI and IBE. In this paper, we propose a new cryptographic primitive, referred to as certificate-based group encryption (CBGE). In this notion, a certificate authority issues the certificate as a part of decryption key corresponding to a user’s public key and other information; and the user can register himself as a group member to a group manager. Then anyone can verifiably send confidential messages to a group member whose identity information is hidden within a group of certified users. If required, the group manager (GM) can trace the receiver. Following this model, we propose a scheme towards CBGE, where the roles of the verifier and the GM are taken by a single entity. We formally prove the scheme is secure in the random oracle model. Unlike the users existing in GE schemes, users in our scheme need not to check the certificates. CBGE provides an implicit certification mechanism and allows a periodical update of certificate status.