The orbital angular momentum (OAM) of vortex beams can be used for information coding, which has important applications in free space optical communications. Nevertheless, the propagation of beams may encounter various random media in actual transmission space, which will distort the wavefront of vortex beam, rendering the ineffectiveness of traditional methods in retrieving the OAM. To tackle this issue, by taking ground glass as a random medium, recognition of OAM of vortex beam from speckle pattern is realized based on deep learning. Moreover, to further upgrade the information coding and transmission capability, recognition of multiple OAMs is examined as well. The results show that the designed network is capable of simultaneously recognizing five OAMs from a single-shot speckle pattern generated by vortex beams through ground glass.