Recently Stochastic Kronecker Graph (SKG), a network generation model, and vertex-centric BSP, a graph processing framework like Pregel, have attracted much attention in the network analysis community. Unfortunately the two are not very well-suited for each other and thus an implementation of SKG on vertex-centric BSP must either be done serially or in an unnatural manner. In this paper, we present a new network generation model, which we call Poisson Stochastic Kronecker Graph (PSKG), that generate edges according to the Poisson distribution. The advantage of PSKG is that it is easily parallelizable on vertex-centric BSP, requires no communication between computational nodes, and yet retains all the desired properties of SKG.