A new image-based robot visual servo control strategy based on a third-order sliding-mode observer (TOSM) model predictive control is proposed in this study. This new control strategy solves the problem of robot visual servo control with system constraints and time-varying disturbances when the camera and model of the robot manipulator are uncertain and the joint velocity is unknown. In the proposed method, the joint velocity and system centralized uncertainties are estimated simultaneously based on a third-order sliding-mode observer, and the image-based visual servoing problem is transformed into a nonlinear optimization problem based on a model predictive control method considering both visibility constraints and actuator constraints, which minimizes the predicted trajectory cost function to generate the control signal for each cycle. Simulations were carried out to verify the effectiveness of the proposed control scheme.