An ink-jet printing apparatus includes a print head having a first discharge port and a second discharge port, a cap, a suction unit connected to the cap for sucking ink from the print head, and a determining unit which determines one to be performed by the print head between a first printing operation using the first and second discharge ports and a second printing operation using the first discharge port only, wherein before the first printing operation, the suction unit is controlled to perform first and second suction operations sucking at different strengths. A storing unit further provided therein stores history information indicating the past performance of that the first printing operation. Before the second printing operation, the suction unit is controlled to perform the first suction operation only and, based on the history information after the printing operation, perform the second suction operation.