The vibration of the surrounding foundation caused by train operation has an important influence on the operational safety and ambient vibration, and its essence is the propagation problem of stress waves generated by moving loads in the foundation. Based on Boit′s theory of saturated poroelastic medium, the dynamic responses of a transversely isotropic (TI) saturated half-space under moving loads are studied. First, the Biot′s equations are transformed into the frequency-wavenumber domain, and then the transformed equations are decoupled to the in-plane part and out-of-plane part through coordinate transformation. Then, the in-plane and out-of-plane wave equations are solved individually by using the potential function method. Finally, substituting the moving loads, the fundamental solutions are expressed as the double Fourier integral with respect to angular frequency and single wavenumber. The correctness of the proposed method is verified by comparing its result with the published one. Numerical calculation and analysis are carried out to discuss the effects of load speed and TI parameters on the half-space dynamic responses. This work provides certain theoretical basis for the vibration control technology of complex site induced by train loads.