This paper studies the spatiotemporal variation of the worldwide air transportation network (WATN) induced by the COVID-19 pandemic in 2020. The variations are captured from four perspectives: passenger throughput, network connectivity, airport centrality, and international connections. Further, this work also considers both global and local connectivity-based metrics for the network analysis. Supported by real-world data, we show that the performance of the WATN has experienced a dynamic pattern of decline and recovery in 2020. Interestingly, the network metrics undergo tremendous variations in a very short period after the World Health Organization declared COVID-19 as a pandemic, with the number of flights and connections dropping by more than 40% within only the first four weeks. Intuitively, the passenger throughput's changing rate is highly correlated to confirmed cases' growth rate during the early period of the COVID-19 outbreak. However, the air transport response to the pandemic condition is very diverse among different countries. The major airports in the WATN fluctuate gradually in different pandemic stages, which is further influenced by the domestic pandemic situation that restricts airport operations. Also, the restoration speed of local connectivity is faster than that of global connectivity because the recovery of international aviation is geographically dependent on different policies of travel restriction, conditional openings, and the number of COVID-19 cases. The analysis deepens our understanding to formulate bilateral policies for pandemic-induced ATN design and management.