In Low Earth Orbit (LEO) satellite networks, satellites operate fast and the inter-satellite link change period is short. In order to sense the spectrum state in LEO satellite networks in realtime, a space-based satellite network intelligent spectrum sensing algorithm based on artificial neural network (ANN) is proposed, while Geosynchronous Earth Orbit (GEO) satellites are introduced to make fast and effective judgments on the spectrum state of LEO satellites by using their stronger arithmetic power. Firstly, the visibility constraints between LEO satellites and GEO satellites are analyzed to derive the inter-satellite link building matrix and complete the inter-satellite link situational awareness. Secondly, an ANN-based energy detection (ANN-ED) algorithm is proposed based on the traditional energy detection algorithm and artificial neural network. The ANN module is used to determine the spectrum state and optimize the traditional energy detection algorithm. GEO satellites are used to fuse the information sensed by LEO satellites and then give the spectrum decision, thereby realizing the inter-satellite spectrum state sensing. Finally, the sensing quality is evaluated by the analysis of sensing delay and sensing energy consumption. The simulation results show that our proposed algorithm has lower complexity, the sensing delay and sensing energy consumption compared with the traditional energy detection method.