In this paper, we propose a convolutional neural network (CNN)-based distributed learning scheme for spectrum sensing in cognitive radio networks (CRN). With the distributed learning architecture, local training is performed on each secondary user (SU) according to its data sample. After model parameters are exchanged between SU and fusion center (FC), model parameter aggregation and update are performed on FC. The CNN model is utilized on each SU and the covariance matrix of received signal is designed as input of CNN. The proposed scheme avoids large amount of traffic transmission in secondary networks during the online detection period, and meanwhile, improves the spectrum sensing performance even under the topology change scenarios. Simulations show that the proposed CNN-based distributed learning spectrum sensing scheme outperforms the conventional sensing algorithms in CRN.