To study the problem of impact time control for missiles in three-dimensional space with field-of-view constraint, a three-dimensional nonlinear sliding mode guidance law was proposed. The sliding mode surface was designed by using the impact time error and then the acceleration commands in pitch and yaw were derived. By making a simple correction to the proposed guidance, the singular issue driven by zero-initial-heading-error was overcome. The stability and convergence of the proposed guidance law was proved in a rigorous mathematical manner. The value range of some certain parameters and the relationship with the pure proportional navigation guidance law and the decoupled three-dimensional guidance law were analyzed. Simulation results indicate that control of the increasing or reducing impact time can be achieved effectively with the field-of-view constraint by using the proposed guidance law. The stronger the degree of coupling between the pitch and yaw planes is, the more advantageous the proposed guidance law in control energy is.