The teleoperation system of mobile manipulator has been widely applied for space exploration, medical assistance, and other fields. To improve operational efficiency, this paper presents a novel prescribed performance synchronization control scheme without applying any approximation functions for a class of teleoperation system of the mobile manipulator with time-varying delays and nonholonomic constraints. Compared with the general manipulator system, the mobile manipulator has a larger workspace and stronger operability. Yet, the heterogeneity of master-slave robots and the nonholonomic constraint of slave robot bring many difficulties to the control of the system. Firstly, a prescribed performance function (PPF) is designed to guarantee that the position synchronization errors are remained within the predetermined boundary and converge to a small preset area within a preset time. Then, the direct force feedback information is introduced into the controller to improve the transparency of the teleoperation. In addition, there are no approximation functions applied in the proposed controller, which can significantly reduce the complexity and computation of the system. Finally, simulation and experimental results are made to illustrate the availability of this method for practical application. Note to Practitioners—The motivation of this paper is to develop an algorithm to improve the steady-state and transient-state performance of mobile manipulator teleoperation system without increasing the complexity of the controller. Compared with the existing works, in this paper, the control algorithm without any approximators is proposed and a time-varying prescribed performance function is introduced, which promotes the steady-state and transient-state performance of the system essentially. At the same time, the introduction of force feedback information improves the transparency of the teleoperation system. The feasibility and effectiveness of the algorithm are verified on...