This paper presents an effective shape image recognition method using the correlation based on 4-dimensional histogram. The histogram-based correlation is accurately applied to express the similarity by comparing the positions of a corresponding dimension between the images, which is calculated by considering 4 directions of the shape image. The correlation measure by using the normalized cross-correlation is also applied to obtain the robust recognition to the geometrical variations such as shape, position, size, and rotation. The proposed method has been applied to the problem for recognizing the 8 shape images of 64*64 pixels and the 30 shape images of 256*256 pixels. The experimental results show that the proposed method has a superior recognition performance that appears the image characters well.