Based on the proximity effect, the exchange interaction at the interface between a ferromagnetic insulator (FI) and a superconductor (S) could enhance the Zeeman splitting of the superconducting quasiparticle density of states. The superconducting electrons feel the exchange field on the surface of the S layer. Therefore, tuning the internal exchange field at the FI/S interface could switch the superconductor from a superconducting state to a normal state, leading to an infinite magnetoresistance in FI/S heterostructure. Here in this work, we fabricate the EuS/Ta heterojunction by the pulsed laser deposition, and perform the magnetotransport measurements. In the EuS/Ta heterojunction, Ta film as a typical BSC supercenter exhibits the superconducting transition under 3.6 K, and the EuS film is ferromagnetic under 20 K. The magnetization of EuS is suppressed by superconductivity of Ta at 0.01 T below 3 K. In addition, the butterfly-type hysteresis loop is observed at 2 K. And the decrease of the saturation magnetization of EuS/Ta heterostructure is observed by comparing with the EuS single layer. It is caused by a reconstruction of homogeneous ferromagnetic order in the EuS ferromagnetic layer due to the proximity effect with the Ta superconducting layer. The above measurement results show that the competition between the ferromagnetism of EuS film and superconductivity of Ta film below T _cof Ta film. If the exchange field of the FI is sufficiently strong, it tries to align the spins of the electrons of a Cooper pair in S layer parallel to each other, thus destroying the superconductivity. Meanwhile, the superconductivity in S layer will be recovered when the exchange field of the FI is weak. The resistance at a specific value of the magnetic field (1 T) steeply drops to zero, and clear hysteresis behavior is observed in EuS/Ta heterostructure, resulting in an infinite magnetoresistance up to 144000%, by tuning the internal exchange field at EuS/Ta interface. Meanwhile, the anomalous Hall effect with hysteresis behavior is observed at 2 K, indicating that the electron in Ta film is spin polarized due to the magnetic proximity effect near the EuS/Ta interface. Our results show that the EuS/Ta heterostructure with infinite magnetoresistance could be a good candidate for spintronic devices.