In a cognitive radio network (CRN), spectrum sensing is an important prerequisite for improving the utilization of spectrum resources. In this paper, we propose a novel spectrum sensing method based on deep learning and cycle spectrum, which applies the advantage of the convolutional neural network (CNN) in an image to the spectrum sensing of an orthogonal frequency division multiplex (OFDM) signal. Firstly, we analyze the cyclic autocorrelation of an OFDM signal and the cyclic spectrum obtained by the time domain smoothing fast Fourier transformation (FFT) accumulation algorithm (FAM), and the cyclic spectrum is normalized to gray scale processing to form a cyclic autocorrelation gray scale image. Then, we learn the deep features of layer-by-layer extraction by the improved CNN classic LeNet-5 model. Finally, we input the test set to verify the trained CNN model. Simulation experiments show that this method can complete the spectrum sensing task by taking advantage of the cycle spectrum, which has better spectrum sensing performance for OFDM signals under a low signal-noise ratio (SNR) than traditional methods.