The time-bound hierarchical key assignment scheme provides a cryptographic solution for the access control problem in distributed systems (e.g., Pay-TV and cloud computing applications). Most time-bound hierarchical key assignment schemes can be divided into two types: adopting tamper-resistant devices and utilizing public values. Despite the fact that adopting tamper-resistant devices can easily resist to collusion attacks, utilizing public values is much cheaper and more suitable for cloud environment. In this paper, we proposed a new time-bound hierarchical key assignment scheme, which can effectively defeat the collusion attack. Besides, the proposed scheme utilizes public values instead of tamper-resistant devices, which will restrict user’s convenience. Compared with the previous works, our scheme requires fewer public values and has better performance.