Clustering research is an important field in machine learning, pattern recognition and other fields. The neutrosophic set characterizes the data through true membership functions, indeterminate membership functions and false membership functions. Data clustering using neutrosophic set has become one of the current research hotspots. In this paper, first, a new definition of data uncertainty in a neutrosophic set is proposed in this paper based on the density of data. Next, a clustering model based on the uncertainty value of neutrosophic set data is proposed by considering the main cluster (true membership) and the noise cluster (false membership) in the data set. The model takes into account the distance of the data points to the cluster centers and the indeterminacy value of each data point, and then minimizes the proposed cost function by the method of Lagrangian multipliers. The true membership value and false membership value of each data point can be obtained. Finally, the effectiveness of the method is demonstrated by experiments on the various datasets. Experimental results show that the cost function has more accurate membership degree when dealing with boundary points and outliers, and outperforms existing clustering methods on datasets.