A fully secure anonymous identity-based broadcast encryption scheme was proposed by combining the Waters dual system encryption with the orthogonality property of composite-order bilinear groups. Based on the standard model without tags, the scheme can achieve constant-size key and ciphertext which constrain three group exponents, respectively. The scheme is proved by using the three static assumptions which do not depend on the number of queries the attacker makes. Furthermore, the analysis results indicate that the scheme proposed in this paper is fully secure and can satisfy the higher efficiency and practice requirement.