For overcoming some defects of existin g image fusion methods based on multi-scale decomposition(MSD) and enhancing th e accuracy of multi-modality images,an adaptive fusion method based on alternat ing non-negative least squares using projected gradient for non-negative matrix factorization (NMF) are proposed in translation invariance nonseparable shearlet transform (TINST) domain.Firstly,the multi-scale and multi-direction decomposi tion for source images is performed by TINST, and a low-frequency and some high-frequency subbands are obtained.Secondly,the low-frequency subband coefficients are regarded as original observed data,which are imposed to iterative operation by alternati ng non-negative least squares using projected gradient for NMF algorithm to obtain fused low-frequency subband coefficients.High-fre quency directional suband coefficients are used as external input excitation in pulse coupled neural networks (PCNN),and after the fire processing and compare-selection operator computing,fused high-frequency directional suband coefficients are obtained.Fin ally,all the fused subbands are reconstructed to an image by inverse TINST.Some fusion experiments on several sets of different modality images are done,and objective performance assessments are implemented f or fused images.The experimental results indicate that the proposed method outperforms a few existing typical fusion techniques ba sed on multi-scale decomposition (MSD) in subjective and objective assessments.