Fuzzy C-means (FCM) clustering algorithm has become one of the commonly used image segmentation techniques with its low learning cost and algorithm overhead. However, the conventional FCM clustering algorithm is sensitive to noise in images. Recently, many of improved FCM algorithms have been proposed to improve the noise robustness of the conventional FCM clustering algorithm, but often at a cost of detail loss on the image. This study presents an improved FCM clustering algorithm based on Lie group theory and applies it to image segmentation. The proposed algorithm constructs matrix Lie group features for the pixels of an image, which summarizes the low-level image features of each pixel and its relationship with other pixels in the neighborhood window. By doing this, the proposed method transforms the clustering problem of measuring the Euclidean distances between pixels into calculating the geodesic distances between Lie group features of pixels on the Lie group manifold. Aiming at the problem of updating the clustering center and fuzzy membership matrix on the Lie group manifold, the proposed method uses an adaptive fuzzy weighted objective function, which improves the generalization and stability of the algorithm. The effectiveness of the proposed method is verified by comparing with conventional FCM and several classic improved algorithms on the experiments of three types of medical images.