Second order statistics of the response of stochastic finite element models can be estimated applying either linear perturbation or Monte Carlo simulation. The former approach is quite convenient from a numerical viewpoint, although its accuracy may be limited; the latter approach can be highly accurate, at the expense of increased numerical costs due to repeated simulation. Hence, this contribution presents a control variates approach that takes advantage of the virtues of both linear perturbation and Monte Carlo simulation, in order to produce estimates of the second order statistics of stochastic finite element models with reduced variability. The application of the proposed approach is illustrated by means of a numerical example.