Wavelet transforms are used for implementing digital watermarking methods in the frequency domain. In this paper, we construct the digital watermarking using various wavelet transforms such as the Daubechies transform, Coiflets transform, Symlets transform and the biorthogonal transform, and we compare each digital watermarking method with the others. We investigate the preservation of the watermark after the data compression attack based on the discrete on the discrete cosine transform. We show that the biorthogonal wavelet, denoted by bior3.5, has the best performance among the wavelet types we selected in an experiment.