In this paper, we show a convergence analysis of extremum seeking control, which is a real-time optimization method for adaptive control, for static systems based on Lyapunov-like analysis. The scheme shown in this paper incorporates an additional element into a conventional extremum seeking scheme, and this enables to guarantee the global convergence of a parameter to an optimal value under some conditions. In this paper, we show conditions of parameters in the extremum seeking to guarantee the global convergence. A numerical result is also shown in this paper.