In recent years, reversible data hiding has attracted much more attention than before. Reversibility signifies that the original media can be recovered without any loss from the marked media after extracting the embedded message. This paper presents a new method that adopts two-level wavelet transform and exploits the feature of large wavelet coefficient variance to achieve the goal of high capacity with imperceptibility. Our method differs from those of previous ones in which the wavelet coefficients histogram not gray-level histogram is manipulated. Besides, clever shifting rules are introduced into histogram to avoid the decimal problem in pixel values after recovery to achieve reversibility. With small alteration of the wavelet coefficients in the embedding process, and therefore low visual distortion is obtained in the marked image. In addition, an important feature of our design is that the use of threshold is much different from previous studies. The results indicate that our design is superior to many other state-of-the-art reversible data hiding schemes.