This paper proposes a reversible watermarking method that embeds binary bits into a digital image by gradient analysis, prediction value computation, two-step embedding process and difference expansion. The gradient analysis is introduced to detect whether a horizontal or vertical edge exists in the pixel context which would improve the accuracy of the prediction value. The two-step embedding process also aims at accurate prediction value computation. Since the prediction error is the key factor in the embedding process, the lower of the prediction error, the better the watermarked image quality. Experimental results show a higher percentage of zeros in the prediction error distribution histogram. Compared with other state-of-the-art reversible watermarking methods, better image quality can be realized by proposed method.