In order to deal with the problems of poor anti-interference, low reconstruction clarity and large errors in the traditional medical image reconstruction methods, we proposed a fuzzy medical images three-dimensional (3D) reconstruction method using quantum algorithm. First of all, a feature matching model of fuzzy medical image was built. Secondly, this study decomposed the edge contour features by using the Gaussian mixture feature matching method, extracted the edge contour vectors of fuzzy medical image, and enhanced the information of fuzzy medical images by adopting the region edge sharpening. Thirdly, this study reorganized the 3D texture structure of images and reconstructed the sparse scattered points according to its texture and detail regions. Finally, we combined with the gray histogram of fuzzy medical images to achieve the adaptive pixel reconstruction of fuzzy medical images, and completed the 3D reconstruction of fuzzy medical images by employing the quantum algorithm. The results show that the proposed method is characterized by high matching degree of image features and balanced distribution of point clouds, and the self-similarity coefficient of the reconstructed texture can reach 0.994; in addition, the SINR value of the reconstruction result can be maintained around 100dB, and it has lower error rate than the traditional method, thereby improving the detection and recognition capability of medical images, and the algorithm has certain practical application.