This paper proposes a modified nonsingular fast terminal sliding mode (NFTSM) guidance law to solve the problem of ground moving target tracking for fixed-wing unmanned aerial vehicle (UAV) in a planar environment. Firstly, the loitering algorithm is analysed, which can steer the UAV to follow and circle around a ground moving target with the desired distance by heading angle control. Secondly, the effects of different parameters on the convergence time of sliding manifold is presented which is helpful for the designing of sliding manifold. Singularity can be avoided by using a modified saturation function which is obtained through a small range around the null point. Moreover, the NFTSM sliding manifold is used in the loitering algorithm. By using the Lyapunov theory, the finite-time convergence of the proposed method has been proved in the the reaching phase and the sliding phase. In order to verify the approach's feasibility and benefits, numerical simulations are performed by using a moving target with three different motion states in comparison with the conventional sliding model control method. Simulation results indicate that, under the proposed NFTSM guidance law, the UAV can reach the desired distance in a short time.