An improved version of a Krylov-Bogoliubov method that gives the approximate solution of the non-linear cubic oscillator ẍ + c 1x + c 3x 3 + ∊f(x, xdot) = 0 in terms of Jacobi elliptic functions is described. Compact general expressions are given for the time derivatives of the amplitude and phase similar to those obtained by the usual Krylov-Bogoliubov method (which gives the approximate solution in terms of circular functions). These expressions are especially simple for quasilinear ( c3 = 0) and quasi-pure-cubic ( c1 = 0) oscillators. Two types of cubic oscillators have been used as examples: the linear damped oscillator f(x, xdot) = xdot, and the van der Pol oscillator f(x, xdot) = (α - βx 2) xdot. The approximate solutions of these quasilinear and quasi-pure-cubic oscillators are simple and accurate. The influence of the non-linearity on the rate of variation of the amplitude of these two types of cubic oscillators was also studied.