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This paper is concerned with the approximation of the radiative transferequation for a grey medium in the slab geometry by the moment method. Wedevelop a novel moment model inspired by the classical $P_N$ model and $M_N$model. The new model takes the ansatz of the $M_1$ model as the weight functionand follows the primary idea of the $P_N$ model to approximate the specificintensity by expanding it around the weight function in terms of orthogonalpolynomials. The weight function uses the information of the first two moments,which brings the new model the capability to approximate an anisotropicdistribution. Mathematical properties of the moment model are investigated, andparticularly the hyperbolicity and the characteristic structure of the Riemannproblem of the model with three moments are studied in detail. Some numericalsimulations demonstrate its numerical efficiency and show its superior incomparison to the $P_N$ model.

A Nonlinear Moment Model for Radiative Transfer Equation in Slab Geometry