The problem of traffic congestion in complex networks is studied. Two kinds of complex network structures, namely random graphs and scale-free networks, are considered. In terms of the structure of connection, random graphs are homogeneous networks whereas the scale-free networks are heterogeneous networks. For both types of networks, we introduce an additional scale-free feature in the load generation process such that a small number of nodes are more heavily loaded than others. A traffic model similar to the routing algorithm in computer networks is used in our simulation study. We show how the network structures and parameters influence the traffic congestion status.