In 2020, people's health suffered a great crisis under the dual effects of the COVID-19 pandemic and the extensive, severe wildfires in the western and central United States. Parks, including city, national, and cultural parks, offer a unique opportunity for people to maintain their recreation behaviors following the social distancing protocols during the pandemic. However, massive forest wildfires in western and central US, producing harmful toxic gases and smoke, pose significant threats to human health and affect their recreation behaviors and mobility to parks. In this study, we employed the geographically and temporally weighted regression (GTWR) Models to investigate how COVID-19 and wildfires jointly shaped human mobility to parks, regarding the number of visits per capita, dwell time, and travel distance to parks, during June - September 2020. We detected strong correlations between visitations and COVID-19 incidence in southern Montana, western Wyoming, Colorado, and Utah before August. However, the pattern was weakened over time, indicating the decreasing trend of the degree of concern regarding the pandemic. Moreover, more park visits and lower dwell time were found in parks further away from wildfires and less air pollution in Washington, Oregon, California, Colorado, and New Mexico, during the wildfire season, suggesting the potential avoidance of wildfires when visiting parks. This study provides important insights on people's responses in recreation and social behaviors when facing multiple severe crises that impact their health and wellbeing, which could support the preparation and mitigation of the health impacts from future pandemics and natural hazards.