In this paper, we consider a delayed predator-prey model with modified Leslie-Gower and Holling type III schemes. By regarding the delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. And we find that Hopf bifurcations can occur as the delay crosses some critical values. In particular, special attention is paid to the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, numerical simulations are carried out to illustrate the main theoretical results.