Many compression methods, lossy or lossless, were developed for 3D hyperspectral images, and various standards have emerged and applied to these amounts of data in order to achieve the best rate-distortion performance. However, high-dimensional data volume of hyperspectal images is problematic for compression and decompression time. Nowadays, fast compression and especially fast decompression algorithms are of primary importance in image data applications. In this case, we present a lossy hyperspectral image compression based on supervised multimodal scheme in order to improve the compression results. The supervised multimodal method is used to reduce the amount of data before their compression with the 3D-SPIHT encoder based on 3D wavelet transform. The performance of the Supervised Multimodal Compression (SMC-3D-SPIHT encoder) has been evaluated on AVIRIS hyperspectral images. Experimental results indicate that the proposed algorithm provides very promising performance at low bit-rates while reducing the encoding/decoding time.