The Cellular Potts Model (CPM) has been widely used for biological simulations. However, most current implementations are either sequential or approximated, which can't be used for large scale complex 3D simulation. In this paper we present a hybrid parallel framework for CPM simulations. The time-consuming PDE solving, cell division, and cell reaction operation are distributed to clusters using the Message Passing Interface (MPI). The Monte Carlo lattice update is parallelized on shared-memory SMP system using OpenMP. Because the Monte Carlo lattice update is much faster than the PDE solving and SMP systems are more and more common, this hybrid approach achieves good performance and high accuracy at the same time. Based on the parallel CPM, we studies the avascular tumor growth using a multiscale model. The application and performance analysis show that the hybrid parallel framework is quite efficient. The hybrid parallel CPM can be used for the large scale simulation (~10-8 sites) of complex collective behavior of numerous cells (~million).