A finite time convergent zero-effort miss guidance law considering the dynamics of the missile autopilot is proposed for the problems of intercepting high speed and maneuvering targets. The three-dimensional relative geometric relation between the missile and target is decoupled. A new three-dimensional zero-effort miss guidance model incorporating the dynamics of the missile autopilot is derived. Based on the adaptive sliding mode control theory and the finite time stability theory, the zero-effort miss in pitch plane and yaw plane is chosen as the sliding mode surfaces, and then the three-dimensional adaptive sliding mode guidance with finite time convergent zero-effort miss is proposed. The guidance law’s stability and finite time convergence ability are analyzed and proved. Simulation results show that the proposed guidance law can achieve the finite time convergence of the zero-effort miss, and has better guidance precision compared with the proportional guidance law.