The properties of the photonic spin Hall effect (PSHE) excited in a prism-coupling waveguide with hyperbolic metamaterial (HMM) are investigated theoretically. The proposed waveguide is composed of four layers including a prism, HMM, thin metal, and air. Both type I and type II HMMs can be created through multilayer realization comprising alternating subwavelength layers of plasma and dielectric or by embedding plasma in a host dielectric matrix, and they are both considered in this study. Our results reveal that the horizontal PSHE shifts in the type I HMM waveguide are significantly suppressed, whereas the horizontal PSHE shifts in the type II HMM waveguide can be enhanced by more than 20 times. The results show that the behavior of vertical PSHE shifts in both types of HMM waveguides are similar and significantly suppressed. The results also show that the HMM and metal layer thicknesses extremely alter the PSHE shifts, especially for the horizontal PSHE shifts in the type II HMM waveguide. Furthermore, the PSHE shifts with different operating wavelengths are calculated and discussed. In addition, the optimal parameters for achieving huge PSHE shifts are explored and presented.