We discuss the computation for ℒ2-induced norms of finite-horizon linear time-varying systems. It is well known that ℒ2-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 ℒ2-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 ℒ2-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.