The low compressive strength of fiber-reinforced polymer (FRP) composites has been one of the critical problems limiting their applications. The compressive damage behaviors of FRP composites are much more complicated than their tensile failure behaviors, usually including different modes, such as delamination and kink-band instability, thereby throwing a great challenge to increase the compressive strength of FRP composites by maneuvering the compressive damage mode. However, limited numerical and experimental studies exist on the compression damage mode control and design. In this study, we examined the competition mechanism between the two major compression damage modes, delamination and kink band, by simulations through finite element method and identified the interlaminar strength and yield strength of the polymer matrix as the crucial factors regulating the damage modes. Accordingly, we established a strategy of designing two material parameters to effectively regulate the compressive damage mode and increase the compressive strength of FRP composites. Furthermore, a series of experiments were conducted to validate the design strategy. The experimental results revealed that tuning the interlaminar strength and yield strength of the polymer matrix could effectively maneuver the compression damage modes and their conversion, and the optimal compressive strength of FPR composites could be achieved when the two damage modes coincide. This study would not only further our understanding of the compressive behaviors of FRP composites but also provide valuable guidelines for their compressive strength enhancement and design.