A new finite-state vector quantization scheme called jigsaw-puzzle vector quantization (JPVQ) is proposed to provide better image quality, especially in the low bit rate context. For low bit rate image coding with conventional finite-state vector quantization (FSVQ) techniques, image quality degrades due to error propagation from one state to the next. The proposed JPVQ algorithm exploits the four-step side-match prediction technique to optimize the spatial continuity of each encoded block to improve the coding performance and reduce the error propagation effect. In the proposed coding scheme, an input block can be encoded by the jigsaw-puzzle block, the dynamic codebook, or the supercodebook. It is demonstrated with experimental results that JPVQ performs significantly better than traditional FSVQ techniques.