Hexagonal image structure represents an image as a collection of hexagonal pixels rather than square pixels in the traditional image structure. However, all the existing hardware for capturing image and for displaying image are produced based on square pixel image structure. Therefore, it becomes important to find a proper software approach to mimic the hexagonal structure so that images represented on the traditional square structure can be smoothly converted from or to the images on the hexagonal structure. For accurate image processing, it is critical to best maintain the image resolution during the image conversion. In this paper, we present an algorithm for bi-cubic interpolation of pixel values on a hexagonal structure when convert from the hexagonal structure to the square structure. We will compare with the results obtained through bi-linear interpolation for the conversion. Our experimental results show that the bi-cubic interpolation outperforms the bi-linear interpolation for most of testing images at the cost of slower and more complex computation.