Provided are an apparatus and method for triangulating a three-dimensional (3D) image, and a computer-readable recording medium storing a computer program for controlling the apparatus. The apparatus includes: a surface expression unit expressing the surface of the 3D image as triangles without holes; and an information output unit outputting a result obtained by the surface expression unit. The apparatus quickly and easily finds surface points and expresses the surface of the 3D image as a combination of triangles reliably, generally, and efficiently, more accurately obtains the 4-sided polygons, reduces the number of holes to be formed, is edited by personally recognizing modification of the surface of the 3D image, and can be used as a tool for expressing intuitive data to edit a dynamic object.