An apparatus for touching a reflection image using an infrared screen, more particularly to an apparatus for touching a reflection image using an infrared screen comprising infrared LEDs, an infrared camera, and a projector for projecting an image in free space so as to implement a virtual touch screen in free space.The apparatus for touching a reflection image using an infrared screen includes: an infrared LED array configured to generate infrared rays and creates an infrared screen in free space, an infrared camera installed such that the lens is directed toward the infrared screen, a projector configured to project an image into the infrared screen, and a space touch sensing module configured to sense a touch location on the infrared screen where user's pointing means is touched using the gray scale image captured by the infrared camera.