Least-squares　reverse　time　migration　(LSRTM)　can　estimate　high-quality　reflectivity　of　subsurface　medium　from　seismic　data.　However,　the　subsurface　reflectivity　depends　on　reflection　angles,　and　its　variations　over　reflection　angles　are　extremely　important　because　they　can　be　used　to　estimate　subsurface　physical　properties　for　seismic　interpretation.　We　present　a　new　formulation　of　the　LSRTM　method　that　can　estimate　reflection-angle-dependent　reflectivity　from　seismic　data.　We　derive　a　forward　modeling　operator　which　predicts　the　reflection　data　without　calculating　the　reflection　angles,　and　verify　that　it　approximately　equals　to　the　reflection-angle-dependent　wave-equation-based　Kirchhoff　modeling　operator　under　the　assumption　that　the　velocity　perturbation　is　small　and　the　reflection　angle　is　smaller　than　the　critical　angle.　Based　on　the　proposed　modeling　operator　associated　with　the　adjoint　of　the　angle-dependent　wave-equation-based　Kirchhoff　modeling　operator,　we　reformulate　LSRTM　as　an　inverse　problem　to　invert　for　reflection-angle-dependent　reflectivity　using　a　preconditioned　conjugate　gradient　algorithm.　The　algorithm　uses　a　low-rank　filter　as　the　preconditioner　to　attenuate　migration　artifacts.　Imaging　tests　on　synthetic　and　field　seismic　data　are　used　to　verify　validity　and　superiority　of　the　proposed　method.　The　tests　illustrate　that　the　proposed　method　can　produce　the　reflection-angle-dependent　reflectivity　with　much　higher　signal-to-noise　ratio　(SNR),　resolution　and　amplitude　fidelity　than　reverse　time　migration.　Compared　with　conventional　LSRTM,　it　can　produce　more　focused　stacked　image　when　the　migration　velocity　contains　errors.　Moreover,　conventional　LSRTM　only　produces　the　angle-independent　reflectivity,　whereas　the　proposed　method　has　the　feasibility　to　produce　the　reflection-angle-dependent　reflectivity.