For prescribed performance control problems of extremum seeking systems based on stable state feasible region constraint, firstly, a new objective function is constructed by using the penalty function, and the extremum reference trajectory is designed. Then, the system equivalent model is constructed by using performance functions and error transformation functions, and the prescribed performance controller is designed by backstepping control. Finally, the uncertain parameter's adaptive estimation law is designed. Extremum seeking is realized and the prescribed performance index is satisfied. Numerical simulation verifies the effectiveness of the proposed method.