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We present a formulation and numerical algorithm to extend the scheme for grey radiation magneto-hydrodynamics (MHD) developed by Jiang (2021) to include the frequency dependence via the multi-group approach. The entire frequency space can be divided into arbitrary number of groups in the lab frame, and we follow the time dependent evolution of frequency integrated specific intensities along discrete rays inside each group. Spatial transport of photons is done in the lab frame while all the coupling terms are solved in the fluid rest frame. Lorentz transformation is used to connect different frames. Radiation transport equation is solved fully implicitly in time while the MHD equations are evolved explicitly so that time step is not limited by the speed of light. A finite volume approach is used for transport in both spatial and frequency spaces to conserve radiation energy density and momentum. The algorithm includes photon absorption, electron scattering as well as Compton scattering, which is calculated by solving the Kompaneets equation. The algorithm is accurate for a wide range of optical depth conditions and can handle both radiation pressure and gas pressure dominated flows. It works for both Cartesian and curvilinear coordinate systems with adaptive mesh refinement. We provide a variety of test problems including radiating sphere, shadow test, absorption of a moving gas, Bondi type flows as well as a collection of test problems for thermal and bulk Compton scattering. We also discuss examples where frequency dependence can make a big difference compared with the grey approach.