In recent years, hydraulic manipulators have been more and more widely used in the field of industrial automation because of their high power-to-weight ratio. Compared with autonomous control, bilateral teleoperation is a more reliable way to operate hydraulic manipulators on harsh occasions. However, teleoperation application in the hydraulic field is still limited due to operation accuracy and master–slave heterogeneous problem. In this paper, a teleoperation framework based on master–slave heterogeneous matching and nonlinear precise motion control for hydraulic manipulator is proposed, including workspace mapping algorithm, velocity-limited interpolator, inverse kinematics solver, trajectory planner, model-based controller, and feedback torque generator. The high-precision teleoperation of the hydraulic manipulator in the situation of master–slave heterogeneity is finally realized based on the designed teleoperation framework. The specialized experiment is set up, and the results also show that the method proposed in this paper can satisfy the teleoperation requirements of the hydraulic manipulator with the maximum operating accuracy up to 0.02 m under the condition of master–slave heterogeneity, which can greatly improve the applicability of hydraulic manipulator teleoperation in the case of master–slave heterogeneity.