Abstract: Incomplete boundary boxes will be generated in the edge of an image in most cases,when covering the image with boxes of fixed size.An effective method by which these incomplete boundary boxes can be taken into computation has been proposed to improve the performance of computation method of box dimension,based on the digital image processing function of MATLAB.The improved computation method is well suitable for images of different sizes with the use of arithmetic-step box dividing method.The calculated results derived from this method also showed a better accuracy and stability.In addition,a quantitative discussion was made about the factors that influence the computation results such as recursive series of image and resolution.Meanwhile some useful control conditions were proposed.In the end,the improved method was applied to calculate the fractal dimension of frost crystal images under different frosting time and the physical meaning of fractal dimension in describing the frosting phenomenon was explained.