55 years (from May 1957 to November 2013) solar radiation data measured in Beijing are used to establish new daily diffuse solar radiation models (NDDSR models). Based on the comparative analysis of air quality index (AQI), fog and haze, a new method that uses AQI to modify existing daily diffuse solar radiation models and NDDSR models is proposed. The test of recent 3-years (from December 2013 to June 2016) diffuse solar radiation data validation showed that the accuracy of existing daily diffuse solar radiation models are improved based on the AQI modification. For each type of models, NDDSR models are more accurate than existing daily diffuse solar radiation models, and further improved with AQI modification, in which Chandrasekaran & Kumar model and NDDSR modified model 5 are the most accurate. Validation of solar radiation data measured in multiple cities shows that NDDSR models and their modified models have a certain applicability to different regions. If not considering AQI modification, the applicability of NDDSR models is best in Guangzhou, followed by Lanzhou, and Shenyang is relatively worse. If considering AQI modification, the correction effect of NDDSR modified models is best in Shenyang, followed by Guangzhou, and Lanzhou is relatively worse. (C) 2017 Elsevier Ltd.