In this paper, the Goos–Hanchen shift (GHS) at the interface between air and the aluminum zinc oxide (AZO)/ZnO hyperbolic metamaterial (AZO-HMM) is theoretically examined. The results herein show that AZO-HMM can enhance the GHS at the interface to a value at 3 orders of the incident wavelength under special conditions, which is much larger than conventional GHS values. Moreover, the GHS can be tuned to be negative or positive by changing the incident wavelength or the volume fraction of AZO.