2D ferromagnets, such as CrX₃ (X = Cl, Br and I), have been attracting extensive attention since they provide novel platforms to fundamental physics and device applications. Integrating CrX₃ with other electrodes and substrates is an essential step to their device realization. Therefore, it is important to understand the interfacial properties between CrX₃ and other 2D materials. As an illustrative example, we have investigated the heterostructures between CrX₃ and graphene (CrX₃/Gr) by first-principles calculations. We found a unique Schottky contact type with strongly spin-dependent barriers in CrX₃/Gr. This can be understood by synergistic effects between the exchange splitting of the semiconductor band of CrX₃ and interlayer charge transfer. The spin-asymmetry of Schottky barriers may result in different tunneling rates of spin-up and down electrons, and then lead to spin-polarized current, namely the spin-filter (SF) effect. Moreover, by introducing X vacancies into CrX₃/Gr, an ohmic contact forms in the spin-up direction. It may enhance the transport of spin-up electrons, and improve the SF effect. Our systematic study reveals the unique interfacial properties of CrX₃/Gr, and provides a theoretical view of the understanding and designing of spintronic devices based on magnetic vdW heterostructures.