In this paper, a novel classifier, called superimposed sparse parameter (SSP) classifier is proposed for face recognition. SSP is motivated by two phase test sample sparse representation (TPTSSR) and linear regression classification (LRC), which can be treated as the extended of sparse representation classification (SRC). SRC uses all the train samples to produce the sparse representation vector for classification. The LRC, which can be interpreted as L2-norm sparse representation, uses the distances between the test sample and the class subspaces for classification. TPTSSR is also L2-norm sparse representation and uses two phase to compute the distance for classification. Instead of the distances, the SSP classifier employs the SSPs, which can be expressed as the sum of the linear regression parameters of each class in iterations, is used for face classification. Further, the fast SSP (FSSP) classifier is also suggested to reduce the computation cost. A mass of experiments on Georgia Tech face database, ORL face database, CVL face database, AR face database, and CASIA face database are used to evaluate the proposed algorithms. The experimental results demonstrate that the proposed methods achieve better recognition rate than the LRC, SRC, collaborative representation-based classification, regularized robust coding, relaxed collaborative representation, support vector machine, and TPTSSR for face recognition under various conditions.