The geometrical singular perturbation theory has been successfully applied in studying a large range of mathematical biological models with different time scales. In this paper, we use the geometrical singular perturbation theory to investigate a slow-fast Leslie-Gower prey-predator model with Monod-Haldane function response and get some interesting dynamical phenomenons such as singular Hopf bifurcation, canard explosion phenomenon, relaxation oscillation cycle, heteroclinic and homoclinic orbits and the coexistence of canard cycle and relaxation oscillation cycle.
