1. A projection system, comprising: a projection unit configured to project a projected image on a surface for projection; an image capturing unit configured to capture an image-capturing area representing an area in which images are capturable and generate a captured image; an operation detection unit configured to detect any user operation on an operation target image representing a targeted image for the user operation by using the captured image; an image-capturing area coordinates calculation unit configured to calculate image-capturing area coordinates for specifying a position of the image-capturing area in the projected image based on the captured image and the projected image when any user operation is detected for the operation target image; a position determination unit configured to determine a position of the operation target image in the projected image based on the image-capturing area coordinates; a projected image generating unit configured to generate a projected image in which the operation target image is laid out on the determined position; and a projection control unit configured to control the projection unit to project the projected image.