A vector extension of the Set Partitioning in Hierarchical Trees (SPIHT) algorithm, named vector-SPIHT (VSPIHT), using trained classified successive refinement VQ, has recently been proposed. In this work, vector set-partitioning is applied to multispectral image compression, in particular to 24-bit color images. Since the individual spectral components are sufficiently correlated, VSPIHT can effectively exploit both the inter-component redundancy as well as the spatial redundancy within each subband of each component, to yield performance superior to separate scalar SPIHT coding of each component. Adaptive arithmetic coding of the first stage VQ index for each class, as well as the significance information, further improves the performance. Coding results demonstrate that the vector-based approach for color images significantly outperforms the scalar counterpart in the mean-squared-error sense.