Abstract: With the diversification and complexity of data, functional ANOVA model has been studied by more and more scholars and applied to all walks of life. In order to reduce the sensitivity of the model to outliers, we figure out a dependent robust functional ANOVA model with t process for dependent multivariate response variables. To depict dependence between variables and ensure the positive definiteness of the covariance function, random effect variable and convolution method are introduced to construct a covariance function in this paper. In addition, the model introduces the random effect function to describe the individual characteristics of the research object. Statistical properties, such as robustness and information consistency, are also studied, and the feasibility of the model is verified by numerical simulation and example analysis.