Abstract: In the report， the Turing instability of the predator-prey model with Beddington-DeAngelis functional response in free diffusion were studied. The sufficient conditions of dissipation and uniform persistence of the system without free diffusion and the local stability of non-negative equilibrium point were analyzed. The condition of Turing instability of the non-negative equilibrium point of the system were characterized， and the condition for producing the bifurcation parameters of Turing pattern and the corresponding Turing region were determined. The numerical results indicated that the system is stable and the wave chromatic number， bifurcation parameters and cross diffusion coefficient are important factors for the generation of Turing pattern.