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Radio resource allocation (RRA) is essential for providing quality-of-service (QoS) to users in wireless networks. In multimedia DS-CDMA networks, power and rate are key components of RRA. We propose a dynamic power and rate joint allocation algorithm for mobile multimedia DS-CDMA networks based on utility functions. The purpose of the algorithm is to maximize utilities of all users in the system. We decompose the utility optimization problem into two levels of subproblems so that the computational complexity is reduced. With our algorithm, radio resources are dynamically allocated to users according to their QoS requirements, current system load and channel condition. Simulation results show that our algorithm performs efficiently for multimedia traffic in mobile DS-CDMA networks.