This paper presents the problem of finite-time stabilization for vehicle suspension systems with hard constraints based on terminal sliding-mode (TSM) control. As we know, one of the strong points of TSM control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. However, two main problems hindering the application of the TSM control are the singularity and chattering in TSM control systems. This paper proposes a novel second-order sliding-mode algorithm to soften the switching control law. The effect of the equivalent low-pass filter can be properly controlled in the algorithm based on requirements. Meantime, since the derivatives of term with fractional power do not appear in the control law, the control singularity is avoided. Thus, a chattering-free TSM control scheme for suspension systems is proposed, which allows both the chattering and singularity problems to be resolved. Finally, the effectiveness of the proposed approach is illustrated by both theoretical analysis and comparative experiment results.