Energy demand-side management is crucial for deep decarbonization. Consumers’ behavioral intentions and real pro-environmental behaviour have been widely discussed separately. However, few studies assessed the intention-behaviour gap and limited empirical evidence has been provided on how to promote the intention-behaviour on residential electricity demand response (DR) project. Here, we identified four intention-behaviour relationship by k-means cluster and analyzed the impacts of normative social influence and peer influence on the intention and behaviour based on large scale incentive-based DR experiment and matching questionnaires data in China. We found that the intention-behaviour gap exists in 77.94% respondents, only 16.09% respondents belong to inclined actors who has both high intention and high electricity savings behaviour. Peer influence and normative social influence can significantly increase intention to participate the DR project and energy-saving behaviour during peak hours, and the impact is larger for respondents with high family endowments and educational level. Specifically, 30.6% of the electricity saving behaviour has been explained directly by the peer influence, while normative social influence electricity saving behaviour through behavioural intention. Besides these, effort expectancy and facilitating conditions also play an important role in promoting the intention and electricity-saving behaviour. Our study further provides feasible solutions to facilitate the residential DR for policymakers.