We propose an efficient linear similarity metric learning method for face verification called Triangular Similarity Metric Learning (TSML). Compared with the relevant stateof-the-art work, this method improves the efficiency of learning the cosine similarity while keeping effectiveness. Concretely, we present a geometrical interpretation based on the triangle inequality for developing a cost function and its efficient gradient function. We formulate the cost function as an optimization problem and solve it with the advanced L-BFGS optimization algorithm. We perform extensive experiments on the LFW data set using four descriptors: LBP, OCLBP, SIFT and Gabor wavelets. Moreover, for the optimization problem, we test two kinds of initialization: the identity matrix and the WCCN matrix. Experimental results demonstrate that both of the two initializations are efficient and that our method achieves the state-of-the-art performance on the problem of face verification.