In this paper, a kind of rate-dependent Holling-Leslie predator-prey chemotaxis model is studied by using linearization method and local bifurcation theory. We discuss the structure of the normal positive equilibrium point in detail in two dimensional space with the prey-tactic sensitivity coefficient as bifurcation parameter and the bifurcation direction is determined near the bifurcation point. The theoretical results show that chemotactic rejection has an unstable effect and can lead to local bifurcation solutions. Finally, the theoretical prediction is verified by numerical simulation, and it is explained that the biochemical system would change from a homogeneous stable state to an unstable biological phenomenon.