Since positions of artificial satellites are determined and exposed, satellite communication signals are vulnerable to radio frequency jamming, e.g., aerospace tracking telemetry and command (TT&C) systems and global navigation satellite system (GNSS). With the development of the flexible and self-adaptive jamming technology, jamming is increasingly difficult to predict and eliminate. To address this challenge, discovering a available spectrum hole and then changing the communication band is one of the effective anti-jamming methods. In this paper, we study the wide spectrum sensing problem based on a modulated wideband converter structure, and proposed an intelligent compressed spectrum hole detection algorithm for anti-jamming satellite communications. First, by utilizing the inherent sparsity of frequency spectrum, this paper introduces the idea of compressed sensing theory to reduce the sampling rate and hardware requirement. Furthermore, to combine the big data generated in practice and prior domain knowledge, this paper designs a novel learned neural network to learn the mapping relationship between the received signal and spectrum occupying state. Numerical simulation results demonstrate the superiority of the proposed algorithm versus other baseline competitors.