Discretization of the integral anisotropic-scattering term in the equation of radiative transfer will result in two kinds of numerical errors: alterations in scattered energy and asymmetry factor. Though quadrature flexibility with large angular directions and further solid-angle splitting in the finite volume method (FVM) allow for reduction/minimization of these errors, computational efficiency is adversely impacted. A phase-function normalization technique to get rid of these errors is simpler and is applied to the three-dimensional (3-D) FVM for the first time to improve anisotropic radiation transfer computation accuracy and efficiency. FVM results are compared to Monte Carlo and discrete-ordinates method predictions of radiative heat transfer in a cubic enclosure housing a highly anisotropic participating medium. It is found that the FVM results generated using the normalization technique conform accurately to the results of the other two methods with little impact on computational efficiency.