A polynomial nodal model which uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine mesh finite difference solutions of the diffusion and transport equations were used for comparison with the model.