The study of image segmentation is a crucial impression in image processing and computer vision appliances, which segments an input image into distinct non-overlapping homogenous divisions and helps to depict the image more conveniently. To improve the performance of the segmentation of gray-level images by introducing a normalized graph cut measure as a thresholding principle to separate an object from the background based on the neutrosophic membership function. We proposed an innovative neutrosophic approach combining a set of features of some efficient algorithms. The implementation of the proposed algorithm is known as the neutrosophic normalized graph cut (NNGC) method. In the gray image segmentation, the problem of wrongly segmentation and segmentation with low accuracy can identify by using this approach. This proposed algorithm is compared with the fuzzy entropy method, neutrosophic graph cut (NGC), classical graphcut, Otsu, and Kittler method. Moreover, we examine that in most cases, our algorithm gives the lowest absolute error, misclassification error, and higher values of signal to noise ratio values that improve the segmentation process of gray images. Finally, we analyze the change of different parameter values in the NNGC and the effect of the substitutes. Also, we discuss the computational complexity of neutrosophic weight matrix results with a weight matrix (classical) results.