Is environmental improvement due to production constraints or green investment efficiency? What impact do social factors have on green investment efficiency? On this issue, this paper combines the measurement of the slack model (SBM) and the "super efficiency" (DEA) model, based on the panel data of China's large and medium-sized steel enterprises from 2009 to 2017, constructs the corresponding model to evaluate enterprise green investment efficiency, and further studies the impact of social media attention on green investment efficiency. The results show that: Firstly, social media attention has a significant positive effect on enterprise green investment efficiency. Secondly, environmental regulation (ER) has a significant positive effect on enterprise green investment efficiency, and the influence of social media attention on enterprise green investment efficiency is positively regulated by environmental regulation. Thirdly, social media attention has a heterogeneous effect in promoting enterprise green investment efficiency. In terms of scale, the promotion effect of social media attention on green investment efficiency is more significant in large enterprises than in medium-sized enterprises. In terms of ownership, the promotion effect of social media attention on green investment efficiency is more significant for state-owned enterprises than private enterprises. In terms of region, the promotion effect of social media attention on green investment efficiency is more significant in east China than in centeral and west China. This paper aims to provide a reasonable reference for the green transformation of China's heavy polluting enterprises.