Strategy imitation plays a crucial role in evolutionary dynamics when we investigate the spontaneous emergence of cooperation under the framework of evolutionary game theory. Generally, when an individual updates his strategy, he needs to choose a role model whom he will learn from. In previous studies, individuals choose role models randomly from their neighbors. In recent works, researchers have considered that individuals choose role models according to neighbors’ attractiveness characterized by the present network topology or historical payoffs. Here, we associate an individual’s attractiveness with the strategy persistence, which characterizes how frequently he changes his strategy. We introduce a preferential parameter α to describe the nonlinear correlation between the selection probability and the strategy persistence and the memory length of individuals M into the evolutionary games. We investigate the effects of α and M on cooperation. Our results show that cooperation could be promoted when α>0 and at the same time M>1, which corresponds to the situation that individuals are inclined to select their neighbors with relatively higher persistence levels during the evolution. Moreover, we find that the cooperation level could reach the maximum at an optimal memory length when α>0. Our work sheds light on how to promote cooperation through preferential selection based on strategy persistence and a limited memory length.