Convolution Neural Networks (CNN) make breakthrough progress in many areas recently, such as speech recognition and image recognition. A limiting factor for use of CNN in large-scale application is, until recently, their computational expense, especially the calculation of linear convolution in spatial domain. Convolution theorem provides a very effective way to implement a linear convolution in spatial domain by multiplication in frequency domain. This paper proposes an unified one-dimensional FFT algorithm based on decimation-in-time split-radix-2/(2a), in which a is an arbitrary natural number. The acceleration performance of convolutional neural network is studied by using the proposed FFT algorithm on CPU environment. Experimental results on the MNIST database and Cifar-10 database show great improvement when compared to the direct linear convolution based CNN with no loss in accuracy, and the radix-2/4 FFT gets the best time savings of 38.56% and 72.01% respectively. Therefore, it is a very effective way to realize linear convolution operation in frequency domain. © 2017, Science Press. All right reserved.