During the COVID-19 pandemic, scientific collaboration has profoundly influenced the sustainability of human science. The pandemic has exposed the fragility of the global health system, forcing various research institutions to cooperate more actively and giving rise to a pressing inquiry regarding its implications on the patterns of scientific institution collaboration. With this in mind, we investigate 2,252,016 scientific papers between 2019 and 2020 to study this issue from an institution cooperation view. Specifically, by proposing a novel weighted cooperation network and utilizing institution cooperation freshness, we investigate different collaboration patterns and strategies when institutions respond to the pandemic. The results show that the crisis generally promotes both fresh and stable cooperation relationships among institutions, and different fields (e.g., STEM and Humanities) demonstrate different collaboration patterns. During the pandemic, institutions with a strong influence have a variety of cooperation strategies, while institutions with a low influence prefer a conservative strategy. Moreover, institutions participating in COVID-19 research are very cautious in choosing partners, which may originate from the risk of cooperation, e.g., the fluctuation of influence, and the causal inference results also verify this conclusion. Overall, our study reveals the impact of the COVID-19 pandemic on scientific research work, which may pave the way for designing policy when other global crises occur again.