The paper describes an efficient lossy and lossless three dimensional (3D) image compression of hyperspectral images. The method adopts the 3D spatial-spectral hybrid transform and the proposed transform-based coder. The hybrid transforms are that Karhunen-Loève Transform (KLT) which decorrelates spectral data of a hyperspectral image, and the integer Discrete Wavelet Transform (DWT) which is applied to the spatial data and produces decorrelated wavelet coefficients. Our simpler transform-based coder is inspired by Shapiro’s EZW algorithm, but encodes residual values and only implements dominant pass incorporating six symbols. The proposed method will be examined on AVIRIS images and evaluated using compression ratio for both lossless and lossy compression, and signal to noise ratio (SNR) for lossy compression. Experimental results show that the proposed image compression not only is more efficient but also has better compression ratio.