This paper considers the convergence rate of an asymmetric Deffuant-Weisbuch model. The model is composed by finite n interacting agents. In this model, agent i’s opinion is updated at each time, by first selecting one randomly from n agents, and then combining the selected agent j’s opinion if the distance between j’s opinion and i’s opinion is not larger than the confidence radius ε0. This yields the endogenously changing inter-agent topologies. Based on the previous result that all agents opinions will converge almost surely for any initial states, the authors prove that the expected potential function of the convergence rate is upper bounded by a negative exponential function of time t when opinions reach consensus finally and is upper bounded by a negative power function of time t when opinions converge to several different limits.