Minimum　mean　squared　error　(MMSE)　detector　achieves　near-optimal　error　rate　performance　for　massive　multiple-input　multiple-output　(M-MIMO)　systems　but　involves　large-scale　matrix　inversion　operations　with　high　complexity.　Therefore,　several　approximated　matrix　inversion　algorithms　have　been　proposed.　However,　their　convergence　turns　out　to　be　very　slow.　In　this　paper,　a　new　approach　based　on　joint　Jacobi　and　Richardson　method　is　proposed.　We　show　that　the　proposed　method　accelerate　the　convergence　rate　at　low-complexity　for　different　base　station　(BS)-to-user-antenna　ratio　(BUAR).　Moreover,　a　promising　initial　estimate　is　utilized　to　achieve　closer-to-optimal　initialization　for　the　proposed　method.　To　further　accelerate　the　convergence　rate,　we　introduce　a　new　approximated-eigenvalue　based　relaxation　parameter.　The　convergence　proof　of　the　proposed　algorithm　is　also　provided　in　this　work.　We　analyze　the　computational　complexity　of　different　methods　and　demonstrate　the　performance　differences　with　numerical　simulations.　©　2019　IEEE.