In this paper, a novel sliding-mode analysis method is proposed for the traditional sliding-mode-based extremum seeking control (ESC) scheme. Based on the method, a more rigorous and more concise stability proof of the scheme is presented. Furthermore, a novel switching-based ESC scheme is designed by combining traditional sliding-mode-based ESC and a perturbation-based ESC without steady-state oscillation. This proposed scheme can overcome the steady-state oscillation of sliding-mode-based ESC scheme as well as keep rapid, robust convergence. The stability analysis of the proposed scheme is also provided. The simulation examples show the effectiveness and advantages of the scheme.