A hyperspectral interference image compression algorithm based on fast hierarchical alternating least squares nonnegative tensor Tucker decomposition (FHALS-NTD) is proposed. Firstly, the interference hyperspectral image is decomposed by 3-D OPD lifting-based discrete wavelet transform (3D OPT-LDWT) in the OPD direction. Then, the 3D DWT sub-bands decomposed are used as a three order nonnegative tensor, which is decomposed by the proposed FHALS-NTD algorithm to obtain 8 core tensors and 24 unknown component matrices. Finally, to obtain the final compressed bit-stream, each unknown component matrices element is quantized, and each core tensor is encoded by the proposed bit-plane coding of significant coefficients. The experimental results showed that the proposed compression algorithm could be used for reliable and stable work and has good compressive property. In the compression ratio range from 32∶1 to 4∶1, the average peak signal to noise ratio of proposed compression algorithm is higher than 40 dB. Compared with traditional approaches, the proposed method could improve the average PSNR by 1.23 dB. This effectively improves the compression performance of hyperspectral interference image.