It is more likely to prevent the watermark from JPEG-compression attack, when it is embedded into the low-frequency coefficients of DWT. However, embedding the watermark with the same intensity into them may distort the watermarked image to a large extent. To solve this problem, a novel robust image-watermark algorithm is proposed with the characteristics of selective embedding intensity based on the non-uniform partition. Meanwhile, as a balance for filtering attacks, the watermark bits are also embedded into the high-frequency coefficients which have a big magnitude. Besides, in order to increase the anti-cropping function and the security of the algorithm, Arnold Scrambling Algorithm is applied before the watermark is embedded. The results of the experiments have showed that this algorithm is robust against noising attack, filtering attack and cropping attack, especially the JPEG-compression attack and no obvious distortion appeared in the watermarked image.