For a class of strick feedback nonlinear systems with guaranteed prescribed performance, a backstepping controller is designed. The prescribed performance means that the tracking error should converge to an arbitrarily predefined small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. A performance function and an output error transformation are introduced to transform the original ‘constrained’ system into an equivalent ‘unconstrained’ one. Based on the Lyapunov stability theory, a backstepping controller is designed and the system is stable according to the stability analysis. The simulation results show the correctness of proposed scheme.