The　core　computation　load　of　a　constrained　Model　Predictive　Control　(MPC)　problem　with　interior　point　method　is　to　solve　a　linear　equation　during　every　iteration.　According　to　the　specific　feature　from　problem　formulation　for　constrained　MPC,　this　paper　proposed　a　recursive　rank　one　updating　matrix　inversion　algorithm　for　solving　the　linear　equation.　This　algorithm　is　hardware　implementation　oriented.　Its　efficiency　in　implementing　constrained　MPC　is　verified　by　FPGA　implementation　results.　More　over,　some　important　issues　related　to　FPGA　implementation　of　control　algorithms　are　also　investigated　and　discussed.