This paper deals with the stabilization of continuous-time linear time-invariant systems subject to uniform input quantization. Specifically, the right-hand side of the closed-loop system is rewritten as a linear system subject to a discontinuous perturbation due to the quantization error. Then, the controller design is performed to achieve finite-time convergence of the closed-loop trajectories toward a compact invariant set surrounding the origin. Furthermore, a computationally tractable design procedure for the proposed controller based on linear matrix inequalities, and some insights on the simulation of the closed-loop system are presented. In addition, the effectiveness of the proposed control design procedure is shown in a numerical example.