Ultrasound images, having low contrast and noise, adversely impact in the detection of abnormalities. In view of this, an enhancement method is proposed in this work to reduce noise and improve contrast of ultrasound images. The proposed method is based on scaling with neutrosophic similarity score (NSS), where an image is represented in the neutrosophic domain through three membership subsets T, I, and F denoting the degree of truth, indeterminacy, and falseness, respectively. The NSS measures the belonging degree of pixel to the texture using multi-criteria that is based on intensity, local mean intensity and edge detection. Then, NSS is utilized to extract the enhanced coefficient and this enhanced coefficient is applied to scale the input image. This scaling reflects contrast improvement and denoising effect on ultrasound images. The performance of proposed enhancement method is evaluated on clinical ultrasound images, using both subjective and objective image quality measures. In subjective evaluation, with proposed method, overall best score of 4.3 was obtained and that was 44% higher than the score of original images. These results were also supported by objective measures. The results demonstrated that the proposed method outperformed the other methods in terms of mean brightness preservation, edge preservation, structural similarity, and human perception-based image quality assessment. Thus, the proposed method can be used in computer-aided diagnosis systems and to visually assist radiologists in their interactive-decision-making task.