An issue with regards to the predetermined performance control of a class of non-linear pure feedback system is studied.Firstly, to avoid using thecumbersome formula to handle the non-affine structure of the pure feedback system, a type of non-traditional state transformation is proposed and a first order auxiliary system for controlling input is introduced.Secondly, to ensure the predetermined performance of the pure feedback system, a fairly simple Lyapunov function is designed and a new controlling algorithm based on the Backstepping method is proposed.Finally, the simulation results show that, the designed controller is able to make the state of the non-linear system bounded globally, and to guarantee the predetermined performance of the system.Compared with the conventional methods, the approach proposed here can significantly improve the accuracy of the tracking error and have some certain robustness.