BackgroundWith the deepening of China’s aging population, higher demands have been placed on the supply of elderly care services. As one of the main sources of providing elderly care services, the quality of service provided by elderly caring social organizations (SOs) directly affects the quality of life of the elderly. In recent years, mental health issues among the elderly have become increasingly prominent, especially with the onset of the COVID-19 pandemic. Necessitating the need to pay much more attention to the social support and mental health of this population. This study, therefore, explores the mediating role of institutional satisfaction between the social support and anxiety levels of elderly people in Chongqing’s elderly caring SOs.MethodThis study employed a multi-stage stratified random sampling method to survey 1004 service recipients in elderly caring social organizations from July to August 2022. The self-made sociodemographic questionnaire, institutional satisfaction questionnaire, MSPSS, and GAD-7 were used to collect data on sociodemographic characteristics, institutional satisfaction, social support, and anxiety levels of older adults. Exploratory Factor Analysis and Cronbach’s alpha were used to test construct validity and scale reliability, respectively. Data features were described with One-Way Analysis of Variance, while Multiple Linear Regression and Structural Equation Modeling were used to evaluate relationships between social support, institutional satisfaction, and anxiety levels.ResultsThe average institutional satisfaction score for elderly people in elderly caring SOs was 48.14 ± 6.75. Specifically, the satisfaction score for environmental quality and the satisfaction score for service quality were 16.63 ± 2.56 and 31.52 ± 4.76, respectively. In terms of socio-demographic variables, the presence of visits from relatives, personal annual average income, and self-rated health status all have significant effects on anxiety. Elders who receive visits from relatives have lower levels of anxiety compared to those who do not. Personal annual average income and self-rated health status are negatively correlated with anxiety levels. Social support had significant positive effect on institutional satisfaction, while institutional satisfaction had significant negative effect on anxiety. Institutional satisfaction partially mediated the relationship between social support and anxiety.ConclusionsOur research demonstrates that improving the quality of organizational services in elderly caring SOs and increasing institutional satisfaction among the elders has significant potential for reducing anxiety levels among the elderly. Additionally, the social support by visits from family members cannot be overlooked. We encourage increasing the frequency of family visits through various means to enhance the support provided to elderly individuals.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12889-023-15951-x.