Performance enhancement is one of the most important issues in high performance distributed computing systems. In such computing systems, online users submit their jobs anytime and anywhere to a set of dynamic resources. Jobs arrival and processes execution times are stochastic. The performance of a distributed computing system can be improved by using an effective load balancing strategy to redistribute the user tasks among computing resources for efficient utilization. This paper presents a multi-class load balancing strategy that balances different classes of user tasks on multiple heterogeneous computing nodes to minimize the per-class mean response time. For a wide range of system parameters, the performance of the proposed multi-class load balancing strategy is compared with that of the random distribution load balancing, and uniform distribution load balancing strategies using simulation. The results show that, the proposed strategy outperforms the other two studied strategies in terms of average task response time, and average computing nodes utilization.