This paper deals with unit vector control design for multivariable polytopic uncertain systems under saturating actuators. For that purpose, we propose LMI-based conditions to design the unit vector control gain such that the origin of the closed-loop system is finite-time stable. Moreover, an optimization problem is provided to obtain an enlarged estimate of the region of attraction of the equilibrium point for the closed-loop system, where the convergence of trajectories is ensured even in the presence of saturation functions. Numerical simulations illustrate the effectiveness of the proposed approach.