This paper has proposed a new robust hybrid nonlinear guidance law, which accounts for a missile’s terminal line-of-sight (LOS) angle constraint, in order to intercept a non-cooperative maneuvering target. The proposed hybrid nonlinear guidance strategy consists of two phases; in the first phase, a guidance law named PIGL is derived from prescribed performance control and the inertial delay control method. In PIGL, a revised prescribed performance function is put forward, and a prescribed performance controller with unknown uncertainties is then derived. The controller smoothly drives both the LOS angle and its rate to a predesigned small region under unknown uncertainties that are induced by target’s maneuvers within a fixed time. Then, a guidance law named SIGL is activated, which is derived from sliding mode control and inertial delay control. By driving the desired sliding mode variable to zero within a finite time, the SIGL guidance law is able to achieve high terminal interception accuracy. The robustness of both of the proposed sub-guidance laws has been proved explicitly in this paper. The hybrid guidance law has the advantage of a tunable convergence rate of the LOS angle and the rate of the LOS angle at the beginning period, by which an excessive large initial maneuver can be avoided. Meanwhile, the hybrid guidance law also has the advantage of lower sensitivity to errors in the estimation of the time-to-go.