In this paper, a new methodology for taking into account uncertainties in a gearbox transmission system of a horizontal-axis wind turbine is proposed. Gearbox transmission is the major part of the wind turbine's drive train. For a more reasonable evaluation of its dynamic behaviour, the influence of the uncertain parameters should be taken into consideration. The dynamic equations are solved by using the Polynomial Chaos method combined with the ODE45 solver of Matlab. The effects of the random perturbation caused by the aerodynamic torque excitation on the dynamic response of the studied system are discussed in detail. The proposed method is an efficient probabilistic tool for uncertainty propagation. For more accuracy, the Polynomial Chaos results are compared with direct simulations.