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Endocytosis is an essential biological process for the trafficking of macromolecules in cells. In yeast cells, this involves the invagination of a tubular membrane and the formation of endocytic vesicles. The crescent-shaped BAR proteins are generally assumed to squeeze the tubular membrane and pinch off the vesicle. Here, we theoretically investigate how BAR proteins help drive membrane fission via generating anisotropic curvatures. We show that increasing the isotropic spontaneous curvature at a localized region on the side of a tubular membrane cannot induce membrane fission if the coating area is small. However, a tubular membrane coated with proteins that generate anisotropic curvatures are prone to experience an hourglass-shaped or tube-shaped necking process, which leads to membrane fission. In addition, we propose an experimental method to determine the type of anisotropic curvatures of a protein.