An attachable and detachable continuously supplying ink container comprises two or more shell bodies that are separated from each other and substantially sealed. Each shell body is provided with an ink filling port having a cap, an air filter and an ink outlet port. Each shell body may form a continuously supplying ink container after it has been filled with ink. The ink container can supply ink to a corresponding print head or cartridge by means of a tube being connected with its ink outlet port. Each shell body of the ink continuously supplying container is provided with a connecting part for connecting an adjacent shell body of the continuously supplying ink container. Several shell bodies may be connected to each other and form a unit via the connecting parts. Accordingly, this provides convenience of use and a reduction of manufacturing cost and user cost.