The Fuzzy C-Means (FCM) algorithm is widely used in data mining and machine learning. However, the sensitivity of FCM to the initial value and noise inevitably leads to the decline of the clustering effect. In this paper, a new improved fuzzy clustering algorithm is proposed— Robust denoising FCM clustering via L 2 , 1 NMF and local constraint (RFCM- L 2 , 1 NMF). Firstly, RFCM- L 2 , 1 NMF combines the L 2 , 1 NMF that has noise residual estimation with FCM, using the robustness and noise constraint terms of the L 2 , 1 NMF to attenuate the effect of noise on data clustering. Secondly, RFCM- L 2 , 1 NMF uses the low-dimensional representation of L 2 , 1 NMF as the initial value of FCM, which reduces the defects of FCM caused by the initial value to a certain extent, and makes the clustering effect more stable. Furthermore, since the low-dimensional representation of L 2 , 1 NMF is the hub connecting L 2 , 1 NMF and FCM, to obtain a more accurate low-dimensional representation, we construct a new local constraint term in this paper. Finally, experiments on data sets validate that RFCM- L 2 , 1 NMF is superior compared to other state-of-the-art methods.