Scaling and multifractal properties of the hourly PM2.5 average concentration series at the four air monitoring stations of Chengdu (southwestern China) were explored by using a multifractal detrended fluctuation analysis method, during a typical haze episode (from 1 March to 17 March, 2013). Using shuffling procedure and phase randomization procedure, the major sources of multifractality in these PM2.5 series are studied. The results show that the multifractality nature of PM2.5 series is mainly due to long-range correlation. At the same time, the non-Gaussian probability distributions also partly contribute to the multifractal behaviour. The scale-free power laws behaviours are found to govern the cumulative distributions statistics for PM2.5 concentration fluctuations. The temporal evolutions of the multifractality were investigated by the approach of a sliding window. Further, we attempt to find the answers to the following questions: how does long-range correlation and power-law distribution in PM2.5 evolution emerge? It is inviting to do it in a self-organized criticality (SOC) framework, which was specially designed to model the dynamics of complex systems. A novel PM2.5 evolution model is developed on the bases of SOC theory. The model displays robust power law behaviour in certain dynamical region. The self-organized criticality properties of PM2.5 evolution are discussed. This SOC behaviour is related to a statistically steady state that implies the presence of long-range correlation and power-law distribution in PM2.5 evolution during the haze period. It is the stability of SOC that causes the haze period to be sustained for a long time in Chengdu.