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.