In this paper we consider finite-time control problems for linear systems subject to time-varying parametric uncertainties and to exogenous constant disturbances. The main result provided is a sufficient condition for robust finite-time stabilization via state feedback. It can be applied to problems with both non-zero initial conditions and unknown constant disturbances. This condition is then reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed example is presented to illustrate the proposed methodology.