Classical three-variable chaotic system coupling synchronization has been implemented in previous work based on DNA strand displacement (DSD). Herein, by using DSD reactions as the foundation, a proportional integral (PI) controller for chaotic system is introduced to realize the hybrid projective synchronization for different four-variable chaotic systems. DSD-based chaotic systems are composed of catalysis modules, annihilation modules and degradation modules for realizing the construction of chaotic attractors. PI controllers are consist of catalysis, annihilation and adjust DSD modules that are easy to modify and can be added to chaotic system for achieving hybrid projective synchronization. Our work can be acted as the reference for the investigation of chaos synchronization.