A terfminal guidance law is developed for missiles intercepting maneuvering targets with impact angle constraints. A novel nonsingular terminal sliding mode with fixed-time convergence is constructed to avoid the singularity problem while ensuring the sliding surface, LOS angle and the LOS angular rate are fixed-time convergent. The upper-bound of convergence time is independent of the initial states of missiles and targets and can be set in advance. Compared with conventional fixed-time convergence control, the proposed guidance law has a faster convergence rate by regulating the index of the approaching laws of the sliding surface and the LOS angle error. Besides, an extended state observer is introduced to estimate the unknown disturbance caused by the target acceleration, which ensures that the guidance system has a good robustness and avoids the chattering problem. Finally, simulation results indicate that with the proposed guidance law, the missile can intercept the maneuvering targets effectively under different impact angles. Besides, comparisons with other guidance laws show that the proposed guidance law can improve the convergence rate of the guidance system and allow the missie to intercept the targets more accurately in less time.