Subband coding and vector quantization have been shown to be effective methods for coding images at low bit rates. In this paper, we propose a new subband finite-state vector quantization scheme that combines the SBC and FSVQ. A frequency band decomposition of the image is carried out by means of 2D separable quadrature mirror filters, which split the image spectrum into 16 subbands. In general, the 16 subbands can be encoded by intra-band VQ or inter-band VQ. We will use the inter-band VQ to exploit the correlations among the subband images. Moreover, the FSVQ is used to improve the performance by using the correlations of the neighboring samples in the same subband. It is well known that the inter- band VQ scheme has several advantages over coding each subband separately. Our subband- FSVQ scheme not only has all the advantages of the inter-band VQ scheme but also reduces the bit rate and improves the image quality. Comparisons are made between our scheme and some other coding techniques. The new scheme yields a good peak signal-to-noise ratio performance in the region between 0.30 and 0.31 bit per pixel, both for images inside and outside a training set of five 512 X 512 mono-chrome images. In the experiments, the improvement of our scheme over the ordinary VQ without SBC is up to 3.42 dB and over the inter-band VQ is up to 1.20 dB at nearly the same bit rate for the image Lena. The PSNR of the encoded image Lena using the proposed scheme is 32.1 dB at 0.31 bit per pixel.