The paper addresses the challenges of finite-control-set model predictive control in discrete-time linear systems subject to disturbances, focusing on recursive feasibility and stability. The authors propose a novel framework that ensures robust performance under external perturbations while maintaining computational efficiency. Unlike traditional MPC approaches, which often assume ideal conditions, this study considers more general scenarios where disturbances are inevitable, making it applicable to a broader class of real-world systems. The proposed method incorporates a disturbance rejection mechanism and guarantees recursive feasibility, ensuring that the control inputs remain within the finite set of allowable actions at every time step. This is achieved by designing a tightened constraint set that accounts for potential disturbances, thereby preventing constraint violations. Furthermore, the paper establishes practical asymptotic stability for the closed-loop system, demonstrating that the system state converges to a bounded region around the desired equilibrium point despite the presence of persistent disturbances. The effectiveness of the proposed approach is validated through theoretical analysis and numerical simulations.