To efficiently utilize the discriminant information in the range space of locality preserving total scatter, this paper proposes a complete discriminant locality preserving projections (CDLPP) algorithm for face recognition. Since Fisher discriminant analysis and locality preserving projections (LPP) have been widely used in face recognition, CDLPP algorithm integrates them together and analyzes the discriminant information contained in the principal spaces and null spaces of locality preserving within-class scatter, locality preserving between-class scatter and locality preserving total scatter. First, CDLPP algorithm removes the null space of locality preserving total scatter, in which no discriminant information is contained, using singular value decomposition (SVD). Then, regular discriminant features and irregular discriminant features of CDLPP are extracted severally in the null space and principal space of the locality preserving within-class scatter. Finally, both regular discriminant features and irregular discriminant features are concatenated to be used for face recognition. Extensive experiments on ORL face database, FERET subset and PIE subset illustrate that the performances of CDLPP outperform those of current subspace face recognition algorithms, such as LDA, LPP and discriminant LPP, which proves the effectiveness of the proposed algorithm.