For the issue of missile attacking the target with impact angle constraint, a finite-time convergent sliding-mode guidance law with impact angle of the constraint is put forward. First of all, the missile-target relative motion relationship is established, and the guidance law is designed based on the sliding mode variable structure theory by using a fast nonlinear terminal sliding mode surface and selecting adaptive exponential reaching law. Then, the stability of the guidance law is analyzed by using Lyapunov theory, and analysis is also made to the finite-time convergence. Saturation function is used instead of symbolic function to reduce the influence of jitter. Finally, the designed guidance law is compared with the offset proportional guidance law with fall angle constraint. Simulation shows that the designed guidance law has better performance, stronger robustness, and can achieve the requirement of the expected impact angle.