Most of the QoS-based routing schemes proposed so far focus on improving the performance of individual service classes. In a multi-class network where high priority QoS traffic coexists with best-effort traffic, routing decision for QoS sessions will have an effect on lower ones. A mechanism that allows dynamic sharing of link resources among multiple classes of traffic is needed. In this paper we propose a multi-class routing algorithm based on inter-class sharing resources among multiple class of traffic. Our algorithm is based on the concept of "the virtual residual bandwidth," which is derived from the real residual bandwidth. The virtual residual bandwidth is greater than the residual bandwidth when the load of lower priority traffic is light, and smaller when the load of lower priority traffic is heavy. The idea of our approach is simple since the routing algorithm for individual traffic doesn't change, but the only change is the definition of the link cost. We demonstrate through some extensive simulations the effectiveness of our approach when the best effort distribution is uneven and when its load is heavy. Also better performance is noticed when using topology with large number of alternative paths.