Many response‐adaptive randomization procedures have been proposed and studied over the past few decades. However, most of these procedures are based on parametric structure and do not directly apply to nonparametric models. In this paper, we propose a response‐adaptive randomization procedure based on Mann‐Whitney U test statistic. Under widely satisfied conditions, we derive asymptotic properties of the randomization procedure and further obtain power functions in form under Mann‐Whitney U test. Simulations show the proposed procedure is more robust and more ethical than classical response‐adaptive randomization procedures in some circumstances. Advantages of the procedure are also illustrated in a redesigned real clinical trial.