In this paper, we present a convolutional neural network (CNN) approach for the face verification task. We propose a "Siamese" architecture of two CNNs, with each CNN reduced to only four layers by fusing convolutional and subsampling layers. Network training is performed using the stochastic gradient descent algorithm with annealed global learning rate. Generalization ability of network is investigated via unique pairing of face images, and testing is done on AT&T face database. Experimental work shows that the proposed CNN system can classify a pair of 46×46 pixel face images in 0.6 milliseconds, which is significantly faster compared to equivalent network architecture with cascade of convolutional and subsampling layers. The verification accuracy achieved is 3.33% EER (equal error rate). Learning converges within 20 epochs, and the proposed technique can verify a test subject unseen in training. This work shows the viability of the "Siamese" CNN for face verification applications, and further improvements to the architecture are under construction to enhance its performance.