In this paper, we investigate the analysis and control design problem of a finite-time time-varying linear system of which the performance at the terminal moment is concerned. A finite-time gain measure performance index is proposed and the necessary and sufficient condition is provided that guarantees the performance index smaller than a pre-specified value. Based on the performance analysis, sufficient conditions for the control design via both the state and the output feedback are presented in the form of Differential Linear Matrix Inequalities. The proposed design approach is applied to the guidance law design of a terminal guidance system. The simulation experiments are carried out to show the effectiveness of the proposed approach.