When modeling with the collaborative use of multi-frequency information, the issues of inconsistent variable frequencies and the seasonal effects often associated with high-frequency variables arise. To address these, this paper proposes a Seasonal Mixed-Frequency Grey Prediction Model (SMFGM(1,N)). The new model aligns variable frequencies by introducing the Nakagami function, eliminates the seasonal effects of variables based on seasonal factors, and incorporates nonlinear terms to capture the nonlinear impacts of time on the system. Additionally, to identify the lag parameters in the new model, the Nakagami function is combined with the grey relational model to propose a Mixed-Frequency Grey Relational Model, which helps identify the relationships between variables with different frequencies. Finally, using a case study of annual GDP and quarterly tax revenue, the new model is compared with the mixed-frequency data sampling model, other grey prediction models, neural network models, and statistical models. The results demonstrate that the SMFGM(1,N) model has superior modeling performance and effectively addresses the prediction problems of mixed-frequency data with seasonal patterns, providing a new method for modeling multi-frequency information systems.