Blind　image　deblurring　has　been　a　challenging　issue　due　to　the　unknown　blur　and　computation　problem.　Recently,　the　matrix-variable　optimization　method　successfully　demonstrates　its　potential　advantages　in　computation.　This　paper　proposes　an　effective　matrix-variable　optimization　method　for　blind　image　deblurring.　Blur　kernel　matrix　is　exactly　decomposed　by　a　direct　SVD　technique.　The　blur　kernel　and　original　image　are　well　estimated　by　minimizing　a　matrix-variable　optimization　problem　with　blur　kernel　constraints.　A　matrix-type　alternative　iterative　algorithm　is　proposed　to　solve　the　matrix-variable　optimization　problem.　Finally,　experimental　results　show　that　the　proposed　blind　image　deblurring　method　is　much　superior　to　the　state-of-the-art　blind　image　deblurring　algorithms　in　terms　of　image　quality　and　computation　time.