Based on the data from the China Health and Retirement Longitudinal Study (CHARLS) from 2011 to 2020, this paper uses the Latent Growth Curve Models and the Random Intercept Cross-Lagged Panel Model to examine the dynamic change trajectories of cognition and depression of the elderly, as well as their interaction relationship. It also explores the moderating role of social participation in the relationship between cognitive decline and changes of the depression. The results show that there is a general trend of continuous decline in the cognition of the elderly over time, but this trend varies among different groups of people. The dynamic relationship between the cognition and the depression is mainly manifested as a one-way influence of cognitive decline on the risk of depression. The nature of this influence gradually decreases from an adverse effect in the initial stage over time and eventually turns into a "protective" effect. Continuous social participation can effectively moderate the adverse impact of cognitive decline on depression among the elderly, and the corresponding effect is mainly concentrated among the younger elderly. This paper suggests that regular screening for cognitive decline and depression should be carried out for different groups of the elderly, and a long-term mechanism of social participation based on the differentiated needs of the elderly should be established to delay the process of cognitive decline and reduce the risk of depression in the elderly.