This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion.From the Turing theory,it is believed that there is no Turing patte formation for the equal self-diffusion coefficients.However,combined with cross-diffusion,it shows that the system will exhibit spotted patte by both mathematical analysis and numerical simulations.Furthermore,nsynchrony of the predator and the prey in the space.The obtained results show that cross-diffusion plays an important role on the patte formation of the predator-prey system.