Pressure-dependent refractive index of semiconductor germanium (Ge) near the absorption edge has not been well studied theoretically and experimentally to date. In this paper, we present a pressure-dependent refractive index of Ge film near its absorption threshold (about 1550 nm), deduced from the reflectivity of high crystalline Ge film coated on a fiber end. The thin Ge layer is deposited on one end of an optical fiber by using an E-beam evaporation machine equipped with a substrate heater of a quartz halogen lamp. In order to obtain high crystalline film, the quartz halogen lamp heater provides a constant substrate temperature of 450 ℃ during film deposition. After the film forming, the sample is transferred into a muffle furnace with a nitrogen atmosphere and annealed at 600 ℃ for 20 h to guarantee the formation of higher crystalline film. The process of light propagating through the optical fiber and reflecting from the Ge thin-film involves multi-beam interference. An abnormal dispersion is observed in the refractive index spectra of the polycrystalline Ge near the absorption edge. A comparison shows that the refractive index spectrum of the amorphous Ge is normal dispersion. Unlike previously reported results that the pressure-dependent refractive index had a negative value, in our experiment it is observed to be a positive value near the absorption edge. To better understand this phenomenon, we use a critical point model including the pressure effect to successfully fit the experimental data. We obtain an abnormal dispersion range of 1505-1585 nm and a range of negative value of pressure-dependent refractive index of 1500-1580 nm from the critical point model. In this paper, we adopt the method of high crystalline Ge film coated on a fiber end. This method has the advantages of small volume, high precision and strong stability, which can be used to measure the optical properties of many thin film materials under the different conditions (temperature, electric field or magnetic field, etc.). In this work, we obtain the refractive index of the Ge film and its pressure dependence near the C-band of the optical fiber communication, and these results are conducive to optimized design of the Ge-based optical systems near the C-band of the optical fiber communication.