A projection system includes projection units configured to project an image on a projection body; a preparing unit configured to prepare calibration-use images; an extraction unit configured to extract, from each of the calibration-use images, at least grating points indicating a distortion in a projected image of one of the projection units and alignment points of the projected image of the one of the projection units or another one of the projection units; a conversion unit configured to convert, onto a common coordinate system, the grating points of the projected images of the projection units extracted from the calibration-use images, based on alignment points common to the calibration-use images; and a geometric correction coefficient calculation unit configured to calculate a geometric correction coefficient for providing a projection image to be projected from the projection units, based on the grating points on the common coordinate system.