We consider multiple light scattering in a nematic liquid crystal. Using the Monte Carlo method, we calculate for the first time the effect of a magnetic field on the shape of the peak of coherent backscattering taking into account the longrange action of fluctuations of the orientational order and anisotropy of the scattering length. For a small number of initial and final scattering events, we take into account the ordinary mode of light, which is weakly scattered in a nematic liquid crystal (NLC), whereas a strongly scattered extraordinary mode is taken into account for all scattering events. For simplicity, we use a singleconstant approximation of the NLC elastic moduli. We show that the angular shape of the peak of coherent backscattering remains nearly unchanged, whereas the magnetic field and the scattering phase function vary by several orders of magnitude.