We consider a class of linear time-periodic systems in which the dynamical generator A(t) represents the sum of a stable time-invariant operator A(0) and a small-amplitude zero-mean T-periodic operator epsilon A(p)(t). We employ a perturbation analysis to develop a computationally efficient method for determination of the H-2 norm. Up to second order in the perturbation parameter epsilon we show that: (a) the H-2 norm can be obtained from a conveniently coupled system of Lyapunov and Sylvester equations that are of the same dimension as A(0); (b) there is no coupling between different harmonics of A(p)(t) in the expression for the H-2 norm. These two properties do not hold for arbitrary values of epsilon, and their deribvation would not be possible if we tried to determine the H-2 norm directly without resorting to perturbation analysis. Our method is well suited for identification of the values of period T that lead to the largest increase/reduction of the H-2 norm. Two examples are provided to motivate the developments and illustrate the procedure. (C) 2008 Elsevier Ltd. All rights reserved.