Efficient and accurate spectrum sensing is a necessary part in cognitive radio networks. To solve the slow training problem of the traditional machine learning algorithm in spectrum sensing, an orthogonal frequency division multiplexing (OFDM) spectrum sensing method based on convolutional neural networks is proposed. The advantage of deep learning in image processing is applied to the spectrum sensing of OFDM signals. Firstly, the spectrum sensing model of OFDM signals and the cyclic autocorrelation are analyzed. The cyclic autocorrelation is normalized and transformed by the gray level. Then, the convolutional neural network is designed based on the LeNet-5 network to learn the training data for more abstract features hierarchically. Finally, the testing data is input into the trained convolutional neural network model, and the spectrum sensing is completed. Simulation results show that this method can complete the spectrum sensing task of OFDM signals, and has a high detection probability under low signal-to-nose ratio.