The paper proposes a shape-adaptive wavelet coding algorithm for known object of diagnostic region of three-dimensional medical images. The new algorithm only applies to the shape-adaptive transformation of the pixels inside the object for decorrelation. After transformation, the number of coefficients of the object is as many as that of the pixels inside the image area. To achieve a quick and lossless transformation, a novel shape-adaptive wavelet transform based on lifting scheme for arbitrarily shaped object is proposed. By analyzing the location of invalid coefficients transformed, the paper also proposes a modified OB-3DSPECK (object-based set partitioned embedded block coder) method that cancels symbol outputs of invalid block or coefficients outside the object, specifically, only two types of symbols are output to arithmetic coding coder. For object region of three-dimensional medical images, the proposed algorithm supports the lossy-to-lossless embedded en/decoding. Experimental results show that the proposed algorithm outperforms OB-3DSPECK by 0.5dB on the average SNR. Furthermore, because of the reduction of the output of one type symbol, the arithmetic coding becomes optional.