To effectively intercept a low-altitude target in clutter background, a nonsingular fast terminal sliding mode guidance law is designed. The designed guidance law can fully exploit the fast convergence characteristics of linear sliding mode control and the finite-time-convergent characteristics of terminal sliding mode control to ensure that the line-of-sight (LOS) angle converges to a desired angle in a limited time at a faster rate. Utilizing the smooth switching characteristics of the hyperbolic tangent function similar to the saturation function, a finite-time-convergent differentiator is designed. Meanwhile, a new finite-time-convergent disturbance observer designed on the tracking differentiator can effectively track the ideal LOS angular rate, suppress the measurement noise, and make a smooth estimation of the target maneuvering acceleration in clutter background. Combining the estimated value of the disturbance observer, the sign function with switch coefficient is introduced to design a composite nonsingular fast terminal sliding mode guidance law. The simulation results show that the composite guidance law can not only effectively suppress the measurement noise of the LOS angular rate and improve the accuracy of low-altitude target intercepting, but also greatly reduce the energy consumption in the interception process.