A new efficient method to compress images using polynomial curve fitting approximation techniques is presented in this paper. The polynomial curve fitting represents many pixels by a smaller number of polynomial coefficients. The presented method is based on two distinct scanning techniques of the image under compression. In the first technique, we scan the image row by row, and in this case, we use first or second order polynomial to represent the chosen number of pixels from the row. In the second case, we scan the image using a block of pixels with variable dimensions and represent each block by a first order two-dimensional polynomial. Experimentally the method gives an acceptable compression ratio with reasonable reconstructed image quality.