We study spin Hall effect (SHE) of transmitted light in a three-layer waveguide with epsilon-near-zero (ENZ) metamaterial. As the increased loss of anisotropic ENZ metamaterial brings decreased propagation loss for oblique incidence, the transmission of incident light is enhanced which induces a different distribution of transverse shift peaks. Based on simulation results, the influences of ENZ permittivity components and thickness as well as gold layer thickness on transverse shift of left-circularly polarized light in ENZ/Au/ENZ waveguide are analyzed. In order to make our results convincing we make use of alternating thin layers of silver and germanium stacking to construct anisotropic ENZ metamaterial. The transverse shifts of incident light with different ENZ metamaterial and gold layer thicknesses are obtained. Calculation results show the maximum transverse shifts of left-polarized light for linear polarized light can achieve 49.6 microns. Meanwhile, the enhanced SHE of transmitted light is invariant with the variation of gold layer which shows a great tolerance to fabrication error.