Video-object coding is one of the most important functionalities proposed by MPEG-4. We propose a new wavelet method to encode the texture of an arbitrarily shaped object, both for the still and for the video-object. The method uses the shape adaptive wavelet transform (SA-DWT) in MPEG-4 still object coding, but with a computationally more efficient lifting implementation. The transformed object coefficients are then quantized and entropy encoded with a partial bit-plane embedded coder, which greatly improves the coding efficiency. We denote the coding algorithm as the video-object wavelet (VOW) coder. Experimental results show that VOW significantly outperforms MPEG-4 in still-object coding, and achieves a comparable performance in video-object coding in terms of PSNR. Moreover, the VOW decoded object looks better subjectively, with less annoying blocking artifacts than that of MPEG-4.