Inspired by the information processing with binary spikes in the brain, the spiking neural networks (SNNs) exhibit significant low energy consumption and are more suitable for incorporating multi-scale biological characteristics. Spiking Neurons, as the basic information processing unit of SNNs, are often simplified in most SNNs which only consider LIF point neuron and do not take into account the multi-compartmental structural properties of biological neurons. This limits the computational and learning capabilities of SNNs. In this paper, we proposed a brain-inspired SNN-based deep distributional reinforcement learning algorithm with combination of bio-inspired multi-compartment neuron (MCN) model and population coding method. The proposed multi-compartment neuron built the structure and function of apical dendritic, basal dendritic, and somatic computing compartments to achieve the computational power close to that of biological neurons. Besides, we present an implicit fractional embedding method based on spiking neuron population encoding. We tested our model on Atari games, and the experiment results show that the performance of our model surpasses the vanilla ANN-based FQF model and ANN-SNN conversion method based Spiking-FQF models. The ablation experiments show that the proposed multi-compartment neural model and quantile fraction implicit population spike representation play an important role in realizing SNN-based deep distributional reinforcement learning.