A diffusive predator-prey system with time delay and advection is considered. By regarding the conversion delay τ as a main bifurcation parameter, we show that Hopf bifurcation occurs when the parameter τ varies. Then by the improved normal form theory and the center manifold theorem for partial functional differential equations, an algorithm for determining the direction and the stability of Hopf bifurcation is derived. Finally, some numerical simulations are carried out for illustration of the theoretical results.