We proposed the neutrosophic approach for segmenting breast lesions in breast Computer Tomography (bCT) images. The neutrosophic set (NS) considers the nature and properties of neutrality (or indeterminacy), which is neither true nor false. We considered the image noise as an indeterminate component, while treating the breast lesion and other breast areas as true and false components. We first transformed the image into the NS domain. Each voxel in the image can be described as its membership in True, Indeterminate, and False sets. Operations α-mean, β-enhancement, and γ-plateau iteratively smooth and contrast-enhance the image to reduce the noise level of the true set. Once the true image no longer changes, we applied one existing algorithm for bCT images, the RGI segmentation, on the resulting image to segment the breast lesions. We compared the segmentation performance of the proposed method (named as NS-RGI) to that of the regular RGI segmentation. We used a total of 122 breast lesions (44 benign, 78 malignant) of 123 non-contrasted bCT cases. We measured the segmentation performances of the NS-RGI and the RGI using the DICE coefficient. The average DICE value of the NS-RGI was 0.82 (STD: 0.09), while that of the RGI was 0.8 (STD: 0.12). The difference between the two DICE values was statistically significant (paired t test, p-value = 0.0007). We conducted a subsequent feature analysis on the resulting segmentations. The classifier performance for the NS-RGI (AUC = 0.8) improved over that of the RGI (AUC = 0.69, p-value = 0.006).