This work is devoted to solving the control problem of vehicle active suspension systems (ASSs) subject to time-varying dynamic constraints. An adaptive control scheme based on nonlinear state-dependent function (NSDF) is proposed to stabilize the vertical displacement of the vehicle body. It provides a reliable guarantee of driving safety, ride comfort, and operational stability. It is commonly known that in the existing work, either the state constraints are ignored which may reduce the stability and safety of the system, or the virtual controller is subjected to some feasibility conditions affecting real system implementation. In this work, it is the first attempt to directly deal with the time-varying displacement and velocity of the vehicle constraints in ASSs without involving any specific feasibility conditions. A novel coordinate transformation based on the NSDF is introduced and integrated into each step of the backstepping design. Thus, the proposed control scheme not only adapts to the time-varying motion (time-varying vertical displacement and velocity) constraints, but also eliminates the feasibility conditions of the virtual controller without the difficulty of obtaining system parameters. Finally, the control scheme for ASSs used in this work is compared with existing control schemes in order to demonstrate its superiority and rationality.