Recently, the trial that is going to use a virtual reality for mathematics education is performed. In particular, the effect of using for study of the space figure that cannot be expressed on the textbook or the blackboard is expected. In this paper, the learning system possessing the function which projects easily the object that the student imagined on a computer display, and the interface that operates the object intuitively is proposed. This system consists of a box that prints special patterns, a monitor, and a video camera. A 3D object is overlaid on the special box and an image is taken with a video camera in real-time. By moving the special box, it is possible to observe the shape of a 3D object from different viewpoints. From a viewpoint of mathematics education, it is the system that supports from a projection improvement in the capability to imagine a 3D object, and the capability to create the projection of conversely arbitrary objects.