Under the dual pressure of the new generation of information technology and COVID-19, it has become necessary for family small and medium-sized enterprises (SMEs) to implement management innovation. However, family SMEs seem to be inexperienced and unthought-out in their innovation strategy selection, so that implementing management innovation is like a gamble, with some successes and some failures. Therefore, we consider a uniqueness of family businesses that family members have many opportunities and power to influence inno-vation activities to investigate how family businesses choose innovation strategies, and then propose a selection model. In order to better capture family member behavior in management innovation, from the perspective of social emotional wealth (SEW), this paper builds this selection model based on evolutionary game theory to analyze the impact of family member behavior on management innovation, and on this basis, introduces the concept of innovation characteristics, thereby increasing the reliability and explanatory validity of the model. Further, this paper analyzes 8 cases in the evolutionary game model through simulation analysis and addresses the question of whether and how family SMEs can successfully implement management innovation, thus providing reference for the selection of innovation strategy of family businesses. This model demonstrates the impact of SEW preferences and innovation characteristics on management innovation, illustrating the evolu-tionary paths and possible outcomes of innovation practices in different cases. Noteworthily, the proposed se-lection model can be used to simulate and predict the development and outcome of innovation practices in a real -world situation, and then innovation strategies are carefully selected by inspired managers.