The propagation characteristics of oblique incidence terahertz (THz) waves through non-uniform plasma are investigated by the shift-operator finite-difference time-domain (SO-FDTD) method combined with the phase matching condition. The electron density distribution of the non-uniform plasma is assumed to be in a Gaussian profile. Validation of the presented method is performed by comparing the results with those obtained by an analytical method for a homogeneous plasma slab. Then the effects of parameters of THz wave and plasma layer on the propagation properties are analyzed. It is found that the transmission coefficients greatly depend on the incident angle, while the polarization of the incident wave has little influence on the propagation process in the range of frequency consideredr. The results confirm that the THz wave can pass through the plasma sheath effectively under certain conditions, which makes it a potential candidate to overcome the ionization blackout problem.