Corporate alliances have become an important way for firms to share the resources and costs of innovation. However, whether corporate technology alliances can effectively enhance the ambidextrous green innovation (AGI) capabilities of firms is a question that still needs to be answered. Building networks of corporate technology alliances based on joint patent application data from the China National Intellectual Property Administration (CNIPA) for the period of 2015–2019, this study investigated the impact of network centrality and structural hole characteristics on exploitative green innovation (IGI) and exploratory green innovation (RGI) from the perspective of internal and external pressures. The empirical results showed that (1) network centrality and structural holes could promote AGI and that the impact on IGI was greater than that on RGI. However, an examination based on lagged effects found a greater impact on RGI. (2) The impact of alliance networks on AGI was positively moderated by internal and external pressures. (3) There were complementary effects between the internal and external pressures. Our study emphasized that it was important to balance AGI to win short-term and long-term competition.