Abstract: This brief addresses a collective evader-capturing problem for an autonomous surface vehicle (ASV) fleet, where one evader vehicle tries to reach the escaping target before the capturing of multiple pursuer ASVs. Therein, the planned objective for the evader switches between pursuer escaping and target approaching. First, a distributed prescribed-time estimator is designed for the multiple pursuer ASVs to estimate the state of the evader ASV. A switching mechanism is afterwards designed between the evading and the escaping modes of the evader. Then, a prescribed-time evader-capturing control (PTECC) law is established according to the mutual dynamics of the evader and pursuers with the proposed estimator. To technically support the proposed PTECC law, sufficient conditions are derived to ensure the prescribed-time capturing of the evader vessel. The theoretical challenge lies in the prescribe-time stability analysis of by the switching nature of the collective evader-capturing system. Finally, simulations are conducted to verify the effectiveness of the present PTECC law.