A Le Corbeiller oscillator having the Goodwin characteristic is one of the simplest two-stroke oscillator model, its periodic process was discussed by Le Corbeiller and de Figueiredo with the help of Liénard construction-a graphical method[5] in [1] and [2]. In this paper, the above problem is approached from analytic ways. Starting from the Lord Rayleigh type equation: x+f(x)+x=0 (1) by means of the piecewise linear method, the reduced characteristic F(x) is written as f(x)={-2h1x x2x-k x>b, where h1, h2,b, k are constants. By using the point-transformation and sussesor-func-tion theory[3], the author proves that when 0 1 2 1 2, there is an unique and stable periodic solution of (1), and the oscillation has the soft-excitation character.The analytic expressions of the period and waveform for stable periodic solution are also given.