In this paper, a new digital watermarking algorithm using wavelet transform is proposed. Wavelet transform is widely used for image processing, because of its multiresolution characteristic which conforms to the principles of the human visual system(HVS). It is also very efficient for localizing images in the spatial and frequency domain. Since wavelet coefficients can be characterized by the gaussian distribution, the proposed algorithm uses a gaussian distributed random vector as the watermark in order to achieve invisibility and robustness. After the original image is transformed using DWT(Discrete Wavelet Transform), the coefficients of all subbands including LL subband are utilized to equally embed the watermark to the whole image. To select perceptually significant coefficients for each subband, we use level-adaptive thresholding. The watermark is embedded to the selected coeffocoents, using different scale factors according to the wavelet characteristics. In the process of watermark detection, the similarity between the original watermark and the extracted watermark is calculated by using vector projection method. We analyze the performance of the proposed algorithm, compared with other transform-domain watermarking methods. The experimental results tested on various images show that the proposed watermark is less visible to human eyes and more robust to image compressions, image processings, geometric transformations and various noises, than the existing methods.