To provide a liquid storage container equipped with a plug member that can prevent leakage of a liquid from the liquid storage container and can be opened without causing scatter of the liquid, and a liquid ejection apparatus equipped with the liquid storage container. For the purpose, at least one of a connection part of the convex part with the cover part and an apical part of the convex part most apart from the connection part is provided offset from the centroid of the cover part, seen from a direction orthogonal to an opening surface of a supply port in a state that the plug member is mounted on a supply port of the liquid storage container.