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.