Abstract: A non-stationary statistical linearization method is proposed for determining the stochastic response of non-linear singledegree-of-freedom systems，subjected to the combined periodic and non-stationary stochastic excitation. Specifically，assuming the system response as a sum of a periodic and of a zero-mean stochastic component，leads two equivalent coupled differential equations，governing the deterministic and the stochastic component，respectively. The derived stochastic sub-equation under non-stationary zero-mean stochastic excitation is cast into an equivalent linear equation，by resorting to the non-stationary statistical linearization method. The related Lyapunov equation governing the second moment of the linear stochastic response，and the deterministic sub-equation governing the periodic response，are solved simultaneously using standard numerical algorithms. Pertinent Monte Carlo simulation demonstrates the applicability and accuracy of the proposed semi-analytical method.