The aim of the research was to investigate the effect of psychological capital on the motivation of sports participation of the elderly in their free time. The research was applied in terms of purpose and descriptive-correlative in terms of research method and data analysis, and the information was collected in the field. The statistical population of this research includes all elderly people between the ages of 60 and 75 in Mashhad. The sampling method was a two-stage cluster. Considering the unlimited size of the community and assuming more than one hundred thousand people, the sample size was 384 people. In order to measure psychological capital, Lutans et al.'s standard psychological capital questionnaire (2007) was used, and to measure sports participation motivation, Gill et al.'s (1983) sports participation motivation questionnaire was used. Spearman's correlation coefficient and structural equation modeling were used to test the research hypotheses. SPSS22 and SmartPLS3 software were used for data analysis. The results showed that in the self-efficacy variable, the highest correlation between self-efficacy and preparation was 0.873 and the lowest correlation between self-efficacy and situational factors was 0.314. In the hope variable, the highest relationship between hope and preparation was 0.531 and the lowest relationship between hope and situational factors was 0.384. In the resilience variable, the highest relationship between resilience and skill improvement was 0.448 and the lowest relationship between resilience and situational factors was 0.175. In the variable of optimism,