In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is pre- sented using Fourier spectral method that use to discretize the space variable and Leap-frog me- thod scheme for time dependence. Test problems including the single soliton wave motion, inte- raction of two solitary waves and interaction of three solitary waves will use to validate the pro- posed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L and L error norms are computed to study the accuracy and the simplicity of the presented method.