In past years, the problem with nonlinear dimensionality reduction has aroused a great deal of interest in many research fields, including pattern analysis, machine learning, and data mining. However, the general manifold learning methods are not robust on the outliers. In the paper, an outlier detection method, based on reconstruction weights, is proposed. The proposed algorithm constructs local ‘strong’ neighborhoods on each sample point, and computes the reliability score of each sample point using local reconstruction weights, and then detects the outliers using the reliability scores. The advantages of the algorithm are that it has fast computation, low parameter, and low parameter sensitivity. Based on the proposed outlier detection method, the robust Isomap algorithm is proposed in this paper. Experimental results illustrate that the proposed algorithm can detect the outliers efficiently and make the manifold learning methods more robust on the outliers.