Alumni giving has become a main source of income for many colleges and universities in the United States. In this paper, we impose a dynamic linear model to predict the alumni-giving behavior by capturing the dynamic of the university-alumni interactions and use MCMC method to do estimation. In the simulation studies, we demonstrate that MCMC method can provide accurate estimation for model parameters and latent dynamic linear cofficients. We apply the MCMC method to a real alumni giving data between 2009 and 2016 and show that our model can have high accuracy of prediction using the data without missing values.