This paper investigates the formation control problem for a multi-robotic fish system and a distributed event-triggered-based formation control framework is proposed. The framework consists of a communication topology, a distributed formation control law, and a dynamic event-triggered communication mechanism. In particular, a position-based formation control law is presented to drive the multi-robotic fish system to an anticipated configuration based on local measurements while keeping pace with a moving target. Meanwhile, a dynamic event-triggered mechanism is utilized to measure importance of the interactive information and decide the communication timing. The proposed formation control method shows its merits to greatly reduce communication consumption with a limited loss of formation control performance. Finally, simulations with quantitative comparisons are presented to verify the effectiveness of the proposed framework. This formation control framework provides a solid foundation for future marine cooperative control of the multi-robotic fish system.