Ridge regression is utilized to tackle various machine learning tasks due to its simplicity and efficiency, and achieves praiseworthy results. However, when ridge regression is directly applied in clustering it can easily lead to trivial solutions. To address this problem, this paper proposes Robust Uncorrelated ridge Regression with Constraint Graph abbreviated as RURCG. Firstly, the method utilizes the generalized uncorrelated constraints to make the ridge regression embedded in the manifold structure, which guarantees the existence of a closed-form solution for its clustering. Secondly, to avoid the impact of outlier data for clustering, a binary vector is imposed on the error term of the ridge regression. The element values of this vector contain a definite physical meaning, with its value being 1 if the data are normal, otherwise, the value being 0. Next, a Laplace construction is embedded in the ridge regression to obtain the local geometrical structure, which involves the graph matrix containing pairwise constraints and labeling information in order to make the clustering structure more adequate. Finally, an iterative optimization strategy is applied to solve the objective function, and simulation experiments on eight benchmark datasets verify the effectiveness of the proposed method.