Summary: An output-feedback extremum seeking control method with second-order sliding mode is proposed for a class of Single-Input-Single-Output (SISO) nonlinear optimization problems Considering that the system’s states are unmeasurable, the control method uses a simple ramp time function as the reference signal of the system’s output, constructs the sliding mode manifold by using the output tracking error and its derivative, and designs the extremum seeking control law with second-order sliding mode. The stability analysis shows that a nonlinear optimization problem with the proposed control method is possible to achieve an arbitrarily small neighborhood of the desired optimal point under all initial conditions, and all the states in the closed-loop system remain uniformly bounded. Simulation results are presented to illustrate the good performance of the proposed control method.