Due to the scarcity of radio spectrum resources and the growing demand, the use of spectrum sensing technology to improve the utilization of spectrum resources has become a hot research topic. In order to improve the utilization of spectrum resources, this paper proposes a spectrum sensing method that combines information geometry and deep learning. Firstly, the covariance matrix of the sensing signal is projected onto the statistical manifold. Each sensing signal can be regarded as a point on the manifold. Then, the geodesic distance between the signals is perceived as its statistical characteristics. Finally, deep neural network is used to classify the dataset composed of the geodesic distance. Simulation experiments show that the proposed spectrum sensing method based on deep neural network and information geometry has better performance in terms of sensing precision.