The estimation of the low-dimensional subspace data may have serious deviation under lacking of the training samples. In order to solve the problem, a novel regularized neighborhood preserving embedding algorithm based on QR decomposition was proposed. Firstly, a local Laplace matrix was defined to preserve local structure of the original data. Secondly, the eigen spectrum space of within-class scatter matrix was divided into three subspaces, the new eigenvector space was obtained by inverse spectrum model defined weight function and then the preprocess of the high-dimensional data was achieved. Finally, a neighborhood preserving adjacency matrix was defined, the projection matrix obtained by QR decomposition and the nearest neighbor classifier were selected for face recognition. Compared with the Regularized Generalized Discriminant Locality Preserving Projection (RGDLPP) algorithm, the recognition accuracy rate of the proposed method was respectively increased by 2 percentage points, 1.5 percentage points, 1.5 percentage points and 2 percentage points on ORL, Yale, FERET and PIE database. The experimental results show that the proposed algorithm is easy to implement and has high recognition rate relatively under Small Sample Size (SSS).