By utilizing backstepping technique, an H∞ robust controller with improved prescribed performance and dynamic surface control is designed for a class of strict feedback nonlinear systems. The transient and steady state performance for the tracking errors of nonlinear system can be guaranteed by using improved prescribed performance constraint. The dynamic surface control is used to overcome the differential explosion problem in the backstepping procedure. The impacts of uncertainties in the system are attenuated by H∞control. The performance and stability analysis proves that the controller design procedure is simple with low complexity and robustness. Finally, the simulation results verify the effectiveness of the controller. By comparing with the existing method, the proposed method has a faster convergence speed and better steady state performance, and also the controller design process is simpler.