Neighborhood preserving embedding (NPE) has been proposed to encode overall geometry manifold embedding information. However, the class-special structure of the data is destroyed by noise or outliers existing in the data. To address this problem, in this article, we propose a novel embedding approach called robust flexible preserving embedding (RFPE). First, RFPE recovers the noisy data by low-rank learning and obtains clean data. Then, the clean data are used to learn the projection matrix. In this way, the projective learning is totally unaffected by noise or outliers. By encoding a flexible regularization term, RFPE can keep the property of the data points with a nonlinear manifold and be more flexible. RFPE searches the optimal projective subspace for feature extraction. In addition, we also extend the proposed RFPE to a kernel case and propose kernel RFPE (KRFPE). Extensive experiments on six public image databases show the superiority of the proposed methods over other state-of-the-art methods.