We　consider　the　box　constrained　continuous　global　minimization　problem.　We　present　an　auxiliary　function　T(x,　k,　p),　which　has　the　same　global　minimizers　as　the　problem　if　p　is　large　enough.　The　minimization　of　T(x,　k,　p)　can　escape　successfully　from　a　previously　converged　local　minimizer　by　taking　the　value　of　k　increasingly.　We　propose　an　algorithm　to　find　a　global　minimizer　of　the　box　constrained　continuous　global　minimization　problem　by　minimizing　T(x,　k,　p)　dynamically.　Numerical　experiments　on　two　sets　of　standard　testing　problems　show　that　the　algorithm　is　effective,　and　is　competent　with　some　well　known　global　minimization　methods.