Spiking Neural Network (SNN), as a brain-inspired machine learning algorithm, is closer to the computing mechanism of human brain and more suitable to reveal the essence of intelligence compared with Artificial Neural Networks (ANN), attracting more and more attention in recent years. In addition, the information processed by SNN is in the form of discrete spikes, which makes SNN have low power consumption characteristics. In this paper, we propose an efficient and strong unsupervised SNN named BioSNet with high biological plausibility to handle image classification tasks. In BioSNet, we propose a new biomimetic spiking neuron model named MRON inspired by 'recognition memory' in the human brain, design an efficient and robust network architecture corresponding to biological characteristics of the human brain as well, and extend the traditional voting mechanism to the Vote-for-All (VFA) decoding layer so as to reduce information loss during decoding. Simulation results show that BioSNet not only achieves state-of-the-art unsupervised classification accuracy on MNIST/EMNIST data sets, but also exhibits superior learning efficiency and high robustness. Specifically, the BioSNet trained with only dozens of samples per class can achieve a favorable classification accuracy over 80% and randomly deleting even 95% of synapses or neurons in the BioSNet only leads to slight performance degradation.