Developing the technology of reversible data hiding based on video compression standard, such as H.264/advanced video coding, has attracted increasing attention from researchers. Because it can be applied in some applications, such as error concealment and privacy protection. This has motivated us to propose a novel two-dimensional reversible data hiding method with high embedding capacity in this article. In this method, all selected quantized discrete cosine transform coefficients are first paired two by two. And then, each zero coefficient-pair can embed 3 information bits and the coefficient-pairs only containing one zero coefficient can embed 1 information bit. In addition, only one coefficient of each one of the rest coefficient-pairs needs to be changed for reversibility. Therefore, the proposed two-dimensional reversible data hiding method can obtain high embedding capacity when compared with the related work. Moreover, the proposed method leads to less degradation in terms of peak-signal-to-noise ratio, structural similarity index, and less impact on bit-rate increase.