The brain's mystery for efficient and intelligent computation hides in the neuronal encoding, functional circuits, and plasticity principles in natural neural networks. However, many plasticity principles have not been fully incorporated into artificial or spiking neural networks (SNNs). Here, we report that incorporating a novel feature of synaptic plasticity found in natural networks, whereby synaptic modifications self-propagate to nearby synapses, named self-lateral propagation (SLP), could further improve the accuracy of SNNs in three benchmark spatial and temporal classification tasks. The SLP contains lateral pre ( SLPpre ) and lateral post ( SLPpost ) synaptic propagation, describing the spread of synaptic modifications among output synapses made by axon collaterals or among converging synapses on the postsynaptic neuron, respectively. The SLP is biologically plausible and can lead to a coordinated synaptic modification within layers that endow higher efficiency without losing much accuracy. Furthermore, the experimental results showed the impressive role of SLP in sharpening the normal distribution of synaptic weights and broadening the more uniform distribution of misclassified samples, which are both considered essential for understanding the learning convergence and network generalization of neural networks.