This research is concerned primarily with nonlinear oscillations of a modified van der Pol equation. The motion is represented by the harmonic oscillator equation, with the addition of a small nonlinear term. The governing differential equation falls under autonomous category. The solution of the problem is examined utilizing the method of slowly varying amplitude and phase (the Krylov-Bogoliubov-Mitropolsky technique). Stationary values of the amplitude are obtained and discussed their stability. It is noted that the stable limit-cycles of the differential equation in the higher order averaging method can be identified easily from the time derivative of the amplitude function and the sign of its derivative at the stationary value of the amplitude.