This paper proposes a self-constructed Mercer kernel based subspace LDA approach for face recognition. Our self-constructed Mercer (SM) kernel function is constructed from a given block diagonal matrix. The entries of all its block diagonal sub-matrices are equal to 1. It shows that this kind of matrix is a symmetric, positive semi-definite matrix and thus can serve as a kernel matrix. Based on such ad hoc kernel matrix and eigen-value decomposition technique, a nonlinear mapping is designed on the training samples and then extended to the whole feature space using interpolatory strategy. In-depth theoretical analysis demonstrates that the function constructed by dot product of the nonlinear mapping is really a Mercer kernel function.The SM-kernel is applied to our previous kernel subspace LDA (KSLDA) approach for face recognition. Two face databases, namely FERET and AR databases, are selected to evaluate the performance of our SM-kernel. Experimental results show that KSLDA with our SM-kernel outperforms KSLDA with RBF kernel.