This paper proposes a data-driven dual-mode model predictive control method for linear discrete systems with unknown parameters, eliminating the need for system modeling. The proposed method enables optimal tracking of the setpoint under constraints. First, the system's future trajectory is predicted based on limited historical operational data, and a real-time optimized artificial equilibrium point is incorporated into the cost function. Control inputs are then determined by solving an online rolling optimization problem, driving the system into a control-invariant set. Within this invariant set, a dynamic feedback controller is derived using the policy iteration method based on historical operational data, and a static feedforward controller is also obtained, achieving locally optimal control in guiding the system to converge to the equilibrium point. Finally, the stability of the proposed method is proven, and it is applied to a linearized four-tank system. Experimental results demonstrate the effectiveness and feasibility of the proposed method, with reduced overshoot and improved convergence performance.