This paper proposes an adaptive fixed-time command filtering control methods based on backstepping method and fuzzy logic systems for a class of continuous stirred tank reactor systems. The repeated derivation of virtual control signal caused by backstepping is solved by the command filter technology, and the filtering error is eliminated by introducing error compensation mechanism. The nonlinear function of the system is approximated using a fuzzy logic system. Based on the fixed-time control method, the speed of convergence is faster, and the convergence time does not depend on the initial state of the system. The closed-loop stability of the continuous stirred tank reactor system is proved using the Lyapunov theorem. The effectiveness of the proposed control method is verified by Matlab/Simulink simulation experiments. Compared with the existing control methods, the proposed control method has the advantages of simple controller structure, fast convergence speed, high control accuracy and no overshoot.