Aiming at the problem of trajectory following for aerial vehicles, a nonsingular fast terminal sliding mode based trajectory following guidance law was developed. A trajectory following dynamic model with line-of-sight angle constraint considering the autopilot dynamics was established based on a virtual target moving along the desired trajectory. A desired line-of-sight angle was derived for the trajectory following problem. To follow the desired trajectory in finite time without singularity, the nonsingular fast terminal sliding mode control and the dynamic surface technique were used to design the guidance law. The mathematical relationship between the error of line-of-sight angle and the trajectory-following error was presented. The Lyapunov stability theorem was proved that the trajectory-following error was uniformly ultimately bounded. The proposed guidance law was compared with the trajectory shaping path following guidance law. The simulation results showed that the proposed guidance law provides better trajectory-following performance and has a better robustness.