Emerging requirement for higher rate data services and better spectrum efficiency is the main driving force identified for the third generation mobile radio systems. Moreover, it needs the capability of providing predictable qualities of service (QoS) for different applications. To maintain different QoS requirements, mechanisms such as call admission control (CAC) and load control, etc. are needed to achieve the required services. In this paper, we propose a CAC algorithm based on channel assignment in a multi-chip rate direct-sequence CDMA (MCR-DS-CDMA) cellular system supporting multi-rate services. Five multi-MBC (mapping of information bit rates to chip rates) channel assignment schemes and corresponding channel selection rules are proposed herein. Computer simulation, where multimedia applications are considered, is used to evaluate the system performance (e.g., blocking probability and system capacity) with different channel assignment schemes. Numerical results demonstrate that scheme 5 (i.e., Minimum-influence scheme) performs better because it provides the highest system capacity and least blocking probability.