In holographic 3D display and holographic video applications, reducing the amount of information in holograms to meet the requirements of communication bandwidth is an important research task. The wavelet threshold and quantization approaches were used to lossy compress holograms, and the effects of using different wavelet basis thresholds on the reconstructed image quality and compression ratio of holograms were compared and analyzed. The research results show that after lossy compression of the wavelet threshold of off-axis digital hologram, the reconstructed image quality obtained by Haar and db5 wavelet bases is the highest. Its peak signal to noise ratio (PSNR) reaches 26.38 dB, and the compression ratio obtained by using sym2 and db2 wavelet is the highest, reaching 6.68. After lossy compression of the wavelet threshold of phase hologram, the reconstructed image quality obtained by Haar and Daubechies wavelets is the highest, with a PSNR of 32.32 dB. The compression ratio obtained by using the Biorthogonal wavelet is the highest, reaching 4.47. The research results provide a reference for how to effectively use the wavelet transform to achieve hologram compression.