Abstract: In order to alleviate the computational burden of large CNN (convolutional neural network) models in current face verification systems, convolution theorem was proposed, which suggested that convolution in the spatial domain was equivalent to product in the frequency domain, to speed up the convolutional layers in CNN, and consequently accelerate face verification systems. By transforming time-consuming convolutions into product operations in the frequency domain, much computation was saved without loss of accuracy. The computational complexities of convolution by using the convolution theorem and the direct computation were compared, and the conditions under which acceleration can be achieved by convolution theorem were given. After Fourier transform, the way of fulfillment of the product/sum operations in parallel was explored in detail, with the goal to fully utilize the power of GPU (graphics processing unit). Results show that the proposed algorithm has achieved apparent speedups for some recent face verification models, demonstrating its effectiveness.