Notching equipment for a steel strip, a method of notching a steel strip, a cold rolling equipment, and a method of cold rolling that make it possible to perform cold rolling on a material without weld breaks, even if the material is a brittle material or a high alloy material such as a silicon steel sheet or a high-tensile steel sheet with high Si and Mn contents. The notching equipment includes a shearing device and a grinding device. The shearing device performs shearing on both edge portions in the steel-strip width direction including the joint to form a first notch. The grinding device grinds end surfaces of both the edge portions of the joint in the steel-strip width direction to form a second notch.