[en] In the evolution of cooperation, the motion of players plays an important role. In this paper, we incorporate, into an evolutionary prisoner dilemma's game on networks, a new factor that cooperators and defectors move with different probabilities. By investigating the dependence of the cooperator frequency on the moving probabilities of cooperators and defectors, μ_c and μ_d, we find that cooperation is greatly enhanced in the parameter regime of μ_c<μ_d. The snapshots of strategy pattern and the evolutions of cooperator clusters and defector clusters reveal that either the fast motion of defectors or the slow motion of cooperators always favors the formation of large cooperator clusters. The model is investigated on different types of networks such as square lattices, Erdoes-Renyi networks and scale-free networks and with different types of strategy-updating rules such as the richest-following rule and the Fermi rule. The numerical results show that the observed phenomena are robust to different networks and to different strategy-updating rules.