This paper presents an adaptive fuzzy singularity-free finite-time tracking control scheme for a 1/4 active suspension system (ASS) with asymmetric dead-zone outputs. Firstly, the error conversion method based on the prescribed performance function is used to constrain the full state tracking errors, which avoids the singularity problem in the controller design and ensures the comfort and safety of the vehicle during driving. Then, the fuzzy approximation lemma is applied to handle the unknown nonlinear function and the uncertain term caused by the asymmetric dead-zone output. Moreover, the nonlinear filter is combined with a backstepping method to avert the problem of explosion of complexity which may appears in the backstepping method. In addition, the finite-time stability of the body subsystem is verified by the symmetric barrier Lyapunov function method, and the suspension space constraint condition is obtained by analyzing the zero dynamic performance of the 1/4 ASS. Finally, the effectiveness of the constructed control scheme is verified by simulations.