In practice ， finite-time stability of systems is more practical and economical than the traditional stability due to costs and other constraints. This paper studies the finite-time stability and stabilization for a class of quadratic discrete-time systems. By means of linear matrix inequality ， the design of feedback control gain matrix is converted into the solutions for linear matrix inequalities. Moreover ， sufficient conditions for the finite-time stability of closed-loop systems with state feedback are determined ， and a method to design the feedback control gain matrix is proposed to achieve the finite-time stability of systems. This method is also suitable to deal with the finite-time boundedness of systems with exogenous disturbance. Finally ， numerical examples are used for validation. The consistency of simulation and theoretical analysis results proves the feasibility of the proposed method.