Aiming at the problem of access delay caused by the contention of resource requests from a large-scale distributed Unmanned aerial vehicle (UAV) network leading to unavoidable conflicts, we propose a grant-free access scheme based on the prediction channel. Specifically, we spread the transmit signals over multiple subcarriers by spreading the frequency, and summaries the signal detection problem for grant -free access as a multi-measurement vector (MMV) compression sensing problem. The channel is estimated based on beacon, and the orthogonal approximation message passing (OAMP)-MMV algorithm is used. Sparsity ratio and noise variance are learnt using variational inference (VI). Finally, the likelihood ratio (LLR) is used to identify the active nodes. Simulation results verify that the proposed scheme outperforms various baseline schemes and achieves low-latency and highly reliable random access.