The approximation of the reachable set of a linear control system is studied.Firstly, the continuous system is discretized into a discrete system by using numerical methods for ordinary differential equations.Then an outer projection method based on optimization techniques is proposed to approximate the reachable set of the discrete system.The outer projection method constructs a finite number of projection problems and each one corresponds to a convex optimization problem.The approximation of the reachable set is achieved by solving finite convex optimization problems.Finally, numerical results show the effectiveness of the proposed method.Compared to the methods in the literatures, when solving the same number of convex optimization problems, the approximation set obtained by using the proposed method is better.