Abstract: The first-order neutron transport equation was solved by the least-squares finite element method based on the discrete ordinates discretization. For the traditional source iteration method is very slowly for the optically thick diffusive medium, sometime even divergent especially for the scattering ratio is close to unity, so the acceleration method should be proposed. There is only diffusive synthetical acceleration (DSA) for the discontinuous finite element method (DFEM) and almost no one for the least-squares finite element method. The additive angular dependent rebalance (AADR) acceleration arithmetic and its extrapolate method were given, in which the additive modification was used. It was applied to solve the transport equation with fixed source, fission source, in optically thick diffusive regions and with unstructured-mesh. The numerical results of benchmark problems demonstrate that the arithmetic can shorten the CPU time about 1.5-2 times and give high precise.