Based on the effective medium theory, the hyperbolic dispersion relationship of graphene-dielectric multilayer (GDM) hyperbolic metamaterials (HMMs) in the near-infrared waveband is analyzed. The transfer matrix method (TMM) is optimized. The transmission spectra of GDM-HMMs with different numbers of periods are calculated and analyzed. Based on the Fabry-Perot (F-P) cavity theory, the evolution of transmission spectra is theoretically analyzed, and the hyperbolic dispersion relationship of GDM-HMMs in the near-infrared waveband is verified. The research results show that the large tangential wave vector condition is needed for the realization of electromagnetic wave transmission in GDM-HMMs. The transmission spectral characteristics are influenced by the total number of structural periods, and the F-P cavity theory can be used for the analysis and reverse structural design.