Based　on　the　matrix　hard　thresholding　method,　a　homotopy　method　is　proposed　for　solving　the　matrix　rank　minimization　problem.　This　method　iteratively　solves　a　series　of　regularization　subproblems,　whose　solutions　are　given　in　closed　form　by　the　matrix　hard　thresholding　operator.　Under　some　mild　assumptions,　convergence　of　the　proposed　method　is　proved.　The　proposed　method　does　not　depend　on　a　prior　knowledge　of　exact　rank　value.　Numerical　experiments　demonstrate　that　the　proposed　homotopy　method　weakens　the　affection　of　the　choice　of　the　regularization　parameter,　and　is　more　efficient　and　effective　than　the　existing　sate-of-the-art　methods.　©　2019,　American　Institute　of　Mathematical　Sciences.　All　rights　reserved.