Summary: In this paper, the Turing instability of a Lotka-Volterra predator-prey model with cross-diffusion and harvesting rate is discussed. It is proved that neither linear self-diffusion nor nonlinear SKT self-diffusion can change the stability of this model, but Turing pattern exists in the linear cross-diffusion and SKT cross-diffusion systems. Meanwhile, to illustrate the analysis results, some numerical examples are also included.