Employee safety voice refers to publishing opinions and suggestions related to workplace safety issues. In recent years, it has gradually become a hot topic in the field of organizational safety management research. Voice endorsement is the leader’s positive feedback to employees, and it is a necessary condition and key link for employees to achieve the purpose of voicing. Although there are many types of research on employee safety voice behavior and voice endorsement, few studies have explored the relationship between the two. Therefore, through a paired questionnaire survey of 214 leaders and 344 employees in construction projects, drawing on social exchange theory, using leader-member exchange (LMX) as a mediating variable, we discuss the mechanism of voice endorsement on employee safety voice behavior. The results show that in construction projects, voice endorsement negatively affects employee safety voice behavior and LMX, and LMX positively affects employee safety voice behavior. LMX has a mediating role in the relationship between voice endorsement and employee safety voice behavior. The results of this study can provide useful guidance for improving employee safety voice behavior management.