A method and apparatus for second order prediction are provided. In the decoding method, the reconstruction of decoded picture comprises second order prediction and compensation and second prediction storage. The second order prediction and compensation comprises first prediction and compensation and second prediction and compensation, input of which includes reconstructed first order residue and second order residue. The encoding method comprises second order prediction and second prediction storage. Second order prediction consists of first prediction and second prediction, input of which includes reconstructed first order residue and second order residue, and it will generate bit-stream accordingly. This invention will eliminate redundancy using second order prediction encoding and decoding method, so that coding efficiency will be improved.