To solve the terminal guidance problem of missiles intercepting maneuvering targets, a guidance law with impact angle and field-of-view constraints is designed based on the finite-time sliding mode control theory. Firstly, the terminal guidance problem is transformed into the stability problem of the guidance system with state constraints. And, a new nonsingular terminal sliding mode surface and a time-varying barrier Lyapunov function are given, and a terminal sliding mode guidance law is proposed. In addition, an adaptive estimation of the upper bound of the target acceleration is designed for the uncertainty of the target maneuver. Then, the stability theory proves that the state variables of the guidance system are finally finite-time convergence, and field-of-view constraint will not be violated in the whole guidance process based on the design characteristics of the time-varying barrier Lyapunov function and sliding mode surface. Compared with the existing guidance laws considering field-of-view constraint, the guidance law has no command conversion, which can accelerate the convergence rate of the guidance system and enhance the robustness of the guidance system. Finally, simulation experiments verify the effectiveness of the guidance method.