Aiming at the drawback of conventional algorithms to compress dynamic range and enhance infrared images, which cannot preserve sufficient information of the original image, a new method based on the optimal mapping curve is proposed. The histogram of the original infrared image is convolved with an adaptive Gaussian kernel. Then, the first derivative of the smoothed histogram is utilized to accomplish segmentation of the original image. The segmented image is calculated to obtain an optimal nonlinear mapping curve, and then the enhanced image with low dynamic range is obtained. The experiment based on a large amount of infrared images is carried out and the processing results are evaluated qualitatively and quantitatively. The experimental results show that compared with the existing method, the proposed method can minimize the mean square error of the enhanced image compared with its origin. Meanwhile, it can significantly improve the overall visual effect of the image. This algorithm is fast, highly automotive and suitable for real-time processing of infrared videos.