Time-of-flight spectra of CH4 molecules scattered from a LiF(001) surface have been obtained at various scattering angles by making use of a cross-correlation chopper blade for the [100] and [110] azimuthal directions. The incident translational energies of CH4 molecules are varied in the 190-500 meV range, while the target surface temperature is maintained at 300 K. The experimental results have been examined in relation to the washboard model [J. C. Tully, J. Chem. Phys. 92, 680 (1990)] which is modified here to take into account the speed distribution of incoming molecules. A qualitative agreement on their angular dependence has been obtained both in the mean speed and the energy spread of the scattered CH4 molecules, which reflects the effect of the strong corrugation of the sample surface. Their quantitative differences are partly explained by the translation-rotational excitation of CH4 molecules during collision.