This paper mainly solves the problem of synchronous control of the master-slave manipulator in an underwater teleoperation system with hardware performance limitations, model uncertainties, and unknown external disturbances. Firstly, in order to meet the limitations of hardware conditions such as the motor speed in the hardware platform, and a prescribed performance function(PPF) is proposed to constrain the speed error, effectively improving the transient performance of the system. Secondly, a prescribed-performance-based adaptive nonsingular integral sliding mode controller(ANISMC) is proposed. Compared with the existing integral sliding mode controllers, the controller in this paper has a faster convergence speed. Then, the Lyapunov method is used to prove that the transformation error and the sliding surface can converge to zero within a fixed time, solving the problem that the integral sign is difficult to cancel when the integral sliding mode controller is used to prove fixed-time stability with the Lyapunov method, and there is no need to know the upper limit of uncertainties and disturbances in advance. Finally, the simulation comparison experiment shows the superiority of the proposed PPF-based ANISMC