Satisfiability　(SAT)　and　maximum　satisfiability　(MAX-SAT)　are　difficult　combinatorial　problems　that　have　many　important　real-world　applications.　In　this　paper　we　investigate　the　performance　of　the　dynamic　convexized　method　based　heuristics　on　the　weighted　MAX-SAT　problem.　We　first　present　an　auxiliary　function　which　is　constructed　based　on　a　penalty　function,　and　minimize　the　function　by　a　local　search　method　which　can　escape　successfully　from　previously　converged　local　minimizers　by　increasing　the　value　of　a　parameter.　Two　algorithms　of　the　approach　are　implemented　and　compared　with　the　Greedy　Randomized　Adaptive　Search　Procedure　(GRASP)　and　the　GRASP　with　Path　Relinking　(GRASP　+　PR).　Experimental　results　illustrate　efficient　and　faster　convergence　of　our　two　algorithms.