We present a self-consistent Green's function (SCGF) approach for the Anderson many-impurity model to calculate the band dispersion and density of states near the conduction band edge in GaNxAs1-x dilute nitride alloys. Two different models of the N states have been studied to investigate the band structure of these materials: (1) the two-band model, which assumes all N states have the same energy, E-N; (2) a model which includes a full distribution of N states obtained by allowing for direct interaction between N sites. The density of states, projected onto extended and localised states, calculated by the SCGF two-band model, are in excellent agreement with those previously obtained in supercell calculations and reveal a gap in the density of states just above E-N, in contrast with the results of previous non-self-consistent Green's function calculations. However, including the full distribution of N states in a SCGF calculation removes this gap, in agreement with experiment.