Nano-networks employ novel nano-scale communication techniques. A new example of nano-networks is the artificial neural system where nano-machines are linked to neurons to treat the neurodegenerative diseases. Many of the nano-scale communication techniques are inspired by biological systems. Neuro-spike communication is one example of this communication paradigm which is exploited to transfer vital information through the nervous system by neurons or nano-machines. Neurons and nano-machines exploit spike rate and the temporal coding to transmit information by action potentials. However, the efficiency of these encoding methods decreases when the transmitter and receiver are asynchronous. Synchronization is beyond the capabilities of nano-machines. In this paper, first we propose a mathematical model for the jitter of the neuro-spike communication channel. Next, we propose an asynchronous neuro-spike array-based communication scheme in which the transmission order of the generated spikes by different elements of the nano-machines array is used to convey information. Thus, in this scheme, there is no need for time synchronization between the transmitter and receiver nano-machines. Finally, we evaluate our proposed scheme via numerical results. It can be observed that our scheme improves the communication rate in comparison to other schemes about 50%.