Investigating the interaction between fins can guide the design and enhance the performance of robotic fish. In this paper, we take boxfish as the bionic object and discuss the effect of coupling motion gaits among the two primary propulsors, pectoral and caudal fins, on the heading stability of the body. First, we propose the structure and control system of the bionic boxfish prototype. Second, using a one/two-way fluid–structure interaction numerical method, we analyse the key parameters of the prototype and discuss the influence of pectoral and caudal motion gaits on the hydrodynamic performance. Finally, effect of the pectoral and caudal interactions on heading stability of the prototype is systematically analyzed and verified in experiments. Results show that the course-deviating degree, oscillation amplitudes of yawing, rolling, and pitching exhibited by the prototype are smaller than that caused by single propulsor when the motion gaits of both pectoral and caudal fins are coordinated in a specific range. This paper reveals for the first time the effect of interactions between pectoral and caudal fins, on the stability of body's course by means of Computational Fluid Dynamics and prototype experiments, which provides an essential guidance for the design of robotic fish propelled by multi-fins.