Abstract: In order to solve the problem that the traditional evaluation methods are easily affected by subjective factors and need reference image, a non-reference fusion metric for multi-focus images based on alpha mutual information is presented combining statistical information of images. The properties of conditional Rényi entropy were studied, and alpha mutual information was constructed by using Arimoto scheme. The alpha mutual information of input images and the fused image was calculated, and a non-reference fusion metric for multi-focus images was constructed. The metric was employed to assess the results of different image fusion algorithms. The experimental results demonstrate that the proposed metric can objectively evaluate the performance of multi-focus image fusion compared with other frequently-used fusion metrics.