A three-dimensional (3D) wavelet coder based on 3D significance tree splitting is proposed for hyperspectral image compression. 3D discrete wavelet transform (DWT) is applied to explore the spatial and spectral correlations. Then the 3D significance tree structure is constructed in 3D wavelet domain, and wavelet coefficients are encoded via 3D significance tree splitting. This proposed algorithm does not need to use ordered lists, moreover it has less complexity and requires lower fixed memory than 3D set partitioning in hierarchical trees (SPIHT) algorithm and 3D set partitioned embedded block (SPECK) algorithm. The numerical experiments on AVIRIS images show that the proposed algorithm outperforms 3D SPECK, and has a minor loss of performance compared with 3D SPIHT. This algorithm is suitable for simple hardware implementation and can be applied to progressive transmission.