This paper develops a novel controller design for strict feedback nonlinear systems with constant full state constraints and unknown time-varying full state delays. Lyapunov-Krasovskii functionals (LKFs) are applied to handle the unknown time-varying full state delays. To evade the explosion of complexity, command filters (CFs) are utilized with filter errors compensated by introducing compensating signals. In Lyapunov function-based stability analysis, barrier Lyapunov functions are employed to prove that the compensated tracking errors can be constrained in predetermined constant bound limits through the controller design, where the boundedness proof of all signals in the closed-loop system is further simplified. Simulation experiments verify the effectiveness of the proposed design.