A multi-media multi-rate CDMA network is introduced in this paper. Multi-rate CDMA networks not only can transmit information sources with different data rate but they can also accommodate more users by adjusting the transmission rate. The multi-rate CDMA system is designed as a fixed-chip-rate variable-data-rate system differing the multiple-chip-rate CDMA system introduced. The bit error probability of a multi-rate CDMA based on Gaussian approximation is given to obtain the multiple access capacities (MAC) for different data rate. We consider three types of traffic, voice, high-priority data, and low-priority data and two types of transmission rate in the multi-rate CDMA system. A variable-rate admission policy is proposed for voice users and high-priority data users so that the system can accommodate more users. In this way, the average call blocking probability can be fixed by adjusting the number of users operating in the low data rate. Since two sources are competent for available CDMA codes, the code allocations schemes to voice and high-priority data users may yield different call blocking probability. Five allocation schemes are proposed and investigated in this paper. A parallel queuing model is also presented to evaluate exactly the packet delay and throughput for low-priority data users in both forward and reverse links. Since all low-priority data users compete codes remained unused by voice and high-priority data users, four admissions allocation schemes are proposed and analyzed.