We discuss the computation for L(2)-induced norms of finite-horizon linear time-varying systems. It is well known that L(2)-induced norm calculating problems can be converted into optimal control problems. So, with the help of optimal control algorithms, we propose a numerical technique for L(2)-induced norm computation. Our approach is as follows. First, we present a new computational method for nonlinear optimal control problems that is numerically reliable, stable and robust, analysing the convergence property under some assumptions. Next, by modifying the presented method, we propose an algorithm for the L(2)-induced norm calculation of finite-horizon linear time-varying systems, which is essentially different from all other existing methods. Finally, the effectiveness of our algorithm is demonstrated by simulation.