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• Considered the significant impact of the COVID-19 on electricity load. • Developed a novel method based on multi-task learning using parameters sharing layers. • Used the real mobility data from Google and Apple and load data from large power enterprises and public institutions. • The universally adaptable model can control the forecasting error at a low level in the COVID-19. • Implemented the Shapley additive explanations technology to enhance interpretability. Affected by the new coronavirus (COVID-19) pandemic, global energy production and consumption have changed a lot. It is unknown whether conventional short-term load forecasting methods based on single-task, single-region, and conventional indicators can accurately capture the load pattern during the COVID-19 and should be carefully studied. In this paper, we make the following contributions: 1) A mobility-optimized load forecasting method based on multi-task learning and long short-term memory network is innovatively proposed to alleviate the impact of the COVID-19 on short-term load forecasting. The incorporation of mobility data and data sharing layers potentially reduces the difficulty of capturing the load patterns and improves the generalization of the load forecasting models. 2) The real public data collected from multiple agencies and companies in the United States and European countries are used to conduct horizontal and vertical tests. These tests prove the failure of the conventional models and methods in the COVID-19 and demonstrate the high accuracy (error mostly less than 1%) and robustness of the proposed model. 3) The Shapley additive explanations technology based on game theory is innovatively introduced to improve the objectivity of the models. It visualizes that mobility indicators are of great help to the accurate load forecasting. Besides, the non-synchronous relationships between the indicators' correlations and contributions to the load have been proved. [ABSTRACT FROM AUTHOR]