Climate change dynamics and its irregular behavior has been recognized and documented by scientists. However, little is known about how this dynamic process of climate change affects firms’ green innovation, as the debate surrounding how climate change’s impact on business often centers on the effects of static climatic events. This study disentangles the dynamic process of climate change into two dimensions—speed and irregularity. Based on the attention-based view, we argue that the speed of climate change positively influences firms’ green innovation, while the irregularity of climate negatively impacts it. In addition, we propose that these relationships are contingent on firms’ state ownership. Tests on a sample of Chinese listed firms with 47,265 observations spanning the 2000–2022 period support this framework.