The theoretical unbounded orbital angular momentum (OAM) states can be exploited as data bits in the OAM shift keying (OAM-SK) free-space optical (FSO) communications. In order to cope with the atmospheric turbulence (AT) and misalignment in practical applications, various machine learning algorithms, or neural networks (NNs), have been put forward to decode the OAM states. However, to recognize the hybrid spatial modes representing a large bit states, the massive learnable nodes, longer computation time and more training parameters are required to improve the capability of the NNs, resulting in energy efficiency burden to the hardware device. In this paper, the event-based Spiking Neural Network (SNN) is utilized to recognize the hybrid spatial modes consisting of superposed coaxial LG modes with l ranging from 0 to 9 and p=0, which is termed as Spiking OAM-recognition neural network (Spiking-ORNN). In comparison to the previous solution of running deep neural networks (DNNs) on graphics processing units (GPUs), the neuromorphic solution of running Spiking-ORNN on neuromorphic chips exhibits 4300x higher energy efficiency without obvious sacrifice of recognition accuracy (less than 0.5%). Moreover, we experimentally demonstrate a 10-meter 1024-ary OAM-SK FSO communication for the transmission of an image with a 10-bit grey level, wherein the peak signal-to-noise ratio of the received image can exceed 41.4 dB under the AT of =1e−15 m−2/3. We anticipate that our results can stimulate further researches on the utilization of the brain-like SNN chips to reduce the energy consumptions based on the artificial-intelligence-enhanced optoelectronic systems.