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How to encourage individuals to practice green, low-carbon behaviours as an effective way to achieve energy conservation and emission reduction is a scientific and social problem that urgently requires a solution. Considering that a change in individuals' behaviours can be influenced by herd mentality and their own income, in this study, we propose a game model related to individuals' green behaviours (IGB). We divide the relations between individuals into two categories, namely, strong links and weak links, and set some parameters associated with IGB, such as temptation benefit, stubbornness index, and selection preference. Based on a Monte Carlo simulation method, we analyse the key factors affecting IGB. The results show that individuals' blind acquisition of and belief in external information is not conducive to the diffusion of IGB. In addition, if the income of the individuals who do not adopt green behaviours increases, this can greatly inhibit other individuals from adopting green behaviours. Further comparative analysis of the different structures of the underlying network indicates that higher connectivity heterogeneity in the strong links of a network could promote the diffusion of IGB. Furthermore, when individuals' stubbornness is high, the proportion of individuals who adopt green behaviours could also increase. Finally, we analyse how individuals' connectivity and activity rate affect IGB. The results show that people prefer to adopt green behaviours if they exhibit higher connectivity or a lower activity rate. We analysed the important factors affecting IGB, to provide a corresponding basis for promoting IGB scientifically. Image 1 [ABSTRACT FROM AUTHOR]