With the rapid development of Internet of Things (IoT), low earth orbit (LEO) satellite IoT is expected to provide low power, massive connectivity and wide coverage IoT applications. In this context, this paper provides a massive grant-free random access (GF-RA) scheme for LEO satellite IoT. This scheme does not need to change the transceiver, but transforms the received signal to a tensor decomposition form. By exploiting the characteristics of the tensor structure, a Bayesian learning algorithm for joint active device detection and channel estimation during massive GF-RA is designed. Theoretical analysis shows that the proposed algorithm has fast convergence and low complexity. Finally, extensive simulation results confirm its better performance in terms of error probability for active device detection and normalized mean square error for channel estimation over baseline algorithms in LEO satellite IoT. Especially, it is found that the proposed algorithm requires short preamble sequences and support massive connectivity with a low power, which is appealing to LEO satellite IoT.