Aiming at improving the effect of infrared image, increasing its contrast and clarity and enriching its edge and detail information, an infrared image enhancement method by fusion of linear transformation and local equalization was proposed. According to the intensity distribution of image, adaptive piecewise linear transformation on the intensity of pixel was performed, and local histogram equalization on the image was carried out. Then, the contrast weight, saliency weight and brightness weight of the two enhanced images were calculated, respectively. Finally, multi-scale Laplace pyramid decomposition and Gaussian pyramid decomposition were performed on the enhanced images and the corresponding weights, respectively, and multi-scale linear fusion with the decomposed images and the corresponding weights were performed to obtain the final enhanced image. According to the experimental results, it is confirmed that the effectiveness of proposed method compared to existing methods, the enhanced images go with better visual effect, and the information entropy, average gradient and coefficient of variation are higher than existing methods by more than 9.03%, 23.87% and 9.97%, respectively. This study could improve infrared image enhancement performance more effectively.