Joint photographic experts group (JPEG) is the most widely used image compression format in daily life. Using reversible data hiding (RDH) technology to authenticate its facticity and integrity is of great significance. This study proposes a new RDH method based on JPEG image. In the proposed algorithm, the small non-zero alternating current (AC) coefficientsin each 8×8 sub-block of the JPEG image are paired according to their amplitudes, and a new two-dimensional reversible mapping rule is designed for these paired AC coefficients to embed information, where the rest large non-zero AC coefficients are used for shifting to make room. Moreover, in order to further reduce the ineffective shifts of AC coefficients, a new adaptive frequency selection strategy is also proposed. In each sub-block, the coefficients belonging to different frequency bands are adaptively selected in the embedding process. The experimental results show that the proposed method is superior to the most advanced methods in terms of the visual quality and increase of file storage size.