In a method of providing 3D teeth alignment image display services using a computer system including at least one orthodontist terminal and a server computer connected to a network, a target teeth information on an orthodontic patient may be received from the orthodontist terminal or an orthodontic patient terminal such that three or four images of a display are respectively projected onto a pyramidal three-sided or four-sided projection plate and thus the orthodontic patient checks a 3D hologram of his/her virtually aligned teeth, a virtually aligned teeth information that is obtained based on the target teeth information may be transformed to three-view or four-view image information outputtable by the display such that the virtually aligned teeth information is projectable onto the three-sided or four-sided projection plate, and the three-view or four-view image information may be transmitted to the orthodontist terminal.