Epidemic process on networks is considered. The system is discribed as a metapopulation network in which a node represents subpopulation (e.g., city or school) and is connected to other nodes via undirected links. Particles represent the subject of infection (e.g., individuals) and interact with each other within nodes while migrating from nodes to nodes in the manner of random diffusion. The nonlinear dependence of contact rate within a node on its population size is introduced, according to the recent finding based on emprical phone-call data. The impacts of the nonlinear dependence are investigated for three aspects of epidemic process: epidemic threshold, infection size at stationary state, and transient dynamics.