A new reliable algorithm for computing H-2-norm of linear time-varying periodic (LTP) systems in continuous-time domain is proposed in this article. The solving of H-2-norm is firstly transformed into the solving of the periodic Lyapunov differential equation (PLDE). Then, the key point in this article is that a new method based on the interval mixed energy matrix and the interval transition matrix computed by the structure-preserving Magnus series method is proposed for solving the PLDE. With the solutions of PLDE, the H-2-norm of LTP systems is evaluated by a simple first-order ordinary differential equation. Finally, the effectiveness and the high accuracy of the proposed algorithms are demonstrated by two numerical examples.