To solve control problems of the strict-feedback extremum seeking system with the objective function is limited by the prescribed performance function, extremum seeking control, prescribed performance control and backstepping control are combined, and a novel prescribed performance backstepping control method is proposed. The new performance function constructed for the objective function and functional transformation are used to construct the equivalent simple transformation model, the backstepping controller is designed based on the transformation model and the appropriate Lyapunov function selected by using the recurrence method, and the objective function extremum is searched and prescribed performance index is realized. Simulation result shows the effectiveness of the proposed design method.