Abstract: It is a kind of fundamental work to obtain the dynamic response of a viscoelastic half-space subjected to moving loads for solving the environment vibration problems caused by traffic loads. Although the dynamic response of a viscoelastic half-space under moving loads in an integral form is not hard, the evaluation of these integrals is a formidable task due to the high oscillation and singularity when the loads' speed approaches or exceeds Rayleigh-wave speed. In this paper, the response of a viscoelastic half-space under moving random line loads has been studied, including uniform loads and non-uniform loads. Using the pseudo-excitation method, the stochastic analysis of the system is transformed into deterministic analysis; and then by applying Fourier transformation, the response in an integral form is developed. First, the integration interval is confirmed by visualizing the integrand; and then the oscillation of the integrand can be overcome by adopting adaptive numerically integration algorithm; finally, the numerical results are obtained. For the purpose of verification, the response of a viscoelastic half-space subjected to moving deterministic loads is also evaluated, and the numerical results have a good agreement with those in literatures. Based on the numerical method, the response of a viscoelastic half-space under moving random loads have been calculated, including the subsonic, transonic and supersonic cases. The response's distribution in time and in space as well as the contribution of different moving loads' speeds to the response are analyzed.