A novel lossless adaptive predictive coding scheme is proposed. The proposed coding scheme divides a coding process into two stages, one for the upper bit signal and another for the lower bit signal. The lower bit signal is adaptively encoded, after the upper bit signal is encoded, utilizing the upper bit signal spatial direction. In the proposed scheme, the predictor and entropy coders are designed to maximize their efficiency for encoding multilevel fingerprint images. The coding efficiency obtained by this scheme is much higher than conventional adaptive predictive coding, as far as multilevel fingerprint images are concerned, providing 9% entropy and 10% average code length reduction. Although the proposed method has been confirmed as being efficient only for encoding multilevel fingerprint images, it can be efficiently applied for encoding ordinary images, such as human faces, natural scenes, and so on, with minor modifications.