This paper investigates the event-triggered-based pursuing and surrounding control of a multi-robotic fish system. A distributed surrounding control framework is put forward to deploy the whole system and enclose the dynamic evader into a convex hull. In particular, distributed kinematics-based motion predictions are hold for common agents in the multi-robotic fish system in addition to the evader. Based on the optimal state estimations, an innovative model-based event-triggered mechanism is tailored rather than frequent interactions to evaluate the importance of the messages. Afterwards, a two-stage position-based surrounding control method is provided. By arbitrating the trade-off between the control performance and interaction frequency, the event-triggered function is regulated to delicately execute the surrounding control task while sharply slashing the interactions. Finally, adequate simulations and experiments are conducted to ensure the effectiveness and robustness of the proposed method. Therefore, whether for communication energy conservation or attack defense, the proposed method shows its significance for future marine assignments.