Analytic formulas for the power spectrum and the bispectrum of galaxies in redshift space are developed on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. We demonstrate the significant contribution of satellite galaxies to the higher multipole power spectrum and bispectrum through the non-linear redshift space distortions of their random motions. We compare behaviors of the multipoles of the bispectrum with results of numerical simulations assuming a halo occupation distribution of the LOWZ sample of the SDSS-III BOSS survey. Our analytic approach is useful to understanding their characteristic properties. We demonstrate that the Fingers of God effect is quite important for the higher multipoles of the power spectrum and the bispectrum in redshift space, depending on the halo occupation distribution parameters.