In this paper, a feature selection framework, called robust feature selection based on intuitionistic hesitant fuzzy cross-correlation coefficients and manifold learning, is constructed. The framework allows the information in high-dimensional data to be effectively used and retained, and ensures the robustness of feature selection. Firstly, the model introduces a dual manifold learning framework that simultaneously performs label and feature manifold learning, preserving the similarity between features and feature weights, as well as the local correlation between samples, respectively. The concept of the intuitionistic hesitant fuzzy cross-correlation coefficient matrix (CCCM) is defined for the first time and the similarity matrix is constructed by using the Yager-type intuitionistic hesitant fuzzy clustering method (YIFCM). Secondly, to achieve a sparse solution of the weight matrix and to ensure the robustness of the model, we employ the \(L_{2,1}\) -norm to constrain the feature weight matrix. Thirdly, a sequence of experiments is carried out on 18 datasets to validate the performance of the 25 comparision models. The results show that the proposed method not only has the best performance on almost all data sets, but also possesses robustness on the data set with doubled noise addition.