In the transformation based compression algorithms of digital hologram for three-dimensional object, the balance between compression ratio and normalized root mean square (NRMS) error is always the core of algorithm development. The Wavelet transform method is efficient to achieve high compression ratio but NRMS error is also high. In order to solve this issue, we propose a hologram compression method using Wavelet-Bandelets transform. Our simulation and experimental results show that the Wavelet-Bandelets method has a higher compression ratio than Wavelet methods and all the other methods investigated in this paper, while it still maintains low NRMS error.