The existing adaptive neighborhood graph embedding method based on local discriminant projection(LADP) only uses discriminant information in the principle space of local within class scatter matrix, which leads to the loss of discriminant information in the null space. To overcome the drawback of LADP, a complete LADP(CLADP) is proposed for face recognition. In the null space of local within class scatter matrix, irregular discriminant features are extracted by maximizing the local between class scatter matrix. In the principle space of local within class scatter matrix, regular discriminant features are extracted by maximizing the local between class scatter matrix and minimizing the local within class scatter matrix. Finally, irregular discriminant features and regular discriminant features are combined as the features of CLADP for face recognition. The experimental results on ORL, Yale face database and PIE subset illustrate the effectiveness of the proposed CLADP.