External disturbances and modeling uncertainties significantly degrade system performance and require efficient control strategies that ensure both robustness and accuracy. A discrete composite control method, termed equivalent input disturbance-improved model predictive control (EID-IMPC), was proposed for precise joint velocity tracking in high-precision motion control. An equivalent input disturbance (EID) estimator and an improved model predictive control (IMPC) controller were integrated to form the proposed control framework. An EID estimator was employed to actively suppress disturbances within the rolling optimization process of model predictive control. Compared with conventional model predictive control, disturbance compensation by the EID estimate and the optimization capability of model predictive control were leveraged to generate constrained and optimal control sequences over the entire prediction horizon. An extended error state and a penalized input soft constraint were introduced in the optimization process to enhance tracking accuracy and ensure smoothness of the control law. Simulation results based on a dual-joint coupled model built in MATLAB demonstrate that the proposed EID-IMPC method maintains excellent tracking performance under complex disturbance conditions, with smooth control inputs that satisfy the imposed constraints. Significant advantages over conventional MPC and other benchmark controllers are demonstrated in terms of joint velocity tracking accuracy, disturbance rejection capability, and control input smoothness, which validates the effectiveness and superiority of the proposed approach. A viable composite control solution is thus provided for engineering applications in high-precision motion control systems.