Aiming at the requirement of the missile terminal impact angle constraint to enhance the damage efficiency, a sliding mode guidance law with impact angle constraint is proposed based on finite-time control and terminal sliding mode control theories. This guidance law chooses terminal sliding mode that contains relative velocity deflection angle and impact angle constraints, and selects the fast power reaching law to ensure that the states of the guidance system are converged in finite time and satisfy the requirement of hit precision and impact angle constraint. The law is analyzed by utilizing the finite-time control theory, thus the finite-time convergent feature of the guidance system states is proved, and the mathematical expression of convergent time is given. Finally, a contrast simulation is made and the simulation results verify the effectiveness, robustness and superiority of the proposed guidance law.