According to this invention, degradation of the image quality of a decoded image is reduced while losslessly encoded data and lossily encoded data coexist. For this purpose, a first encoding unit performs JPEG encoding for each pixel block, and a second encoding unit performs JPEG-LS encoding. Letting Lx be the code length of encoded data generated by the first encoding unit and Ly be the code length of encoded data generated by the second encoding unit, an encoding sequence control unit selects one of the two encoded data and stores the selected data in a first memory in accordance with whether Lx and Ly satisfy a predetermined non-linear boundary function f( ): Ly.gtoreq.f(Lx). At this time, when the axis of abscissas represents the code length of the encoded data generated by the second encoding unit and the axis of ordinates represents that of the encoded data generated by the first encoding unit, the non-linear boundary function f( ) has a curved portion at the two code lengths.