This paper proposes a joint model based on the generalized LASSO to smooth a time-varying graph. The model generalizes the gLASSO from a purely spatial setting to a spatial-temporal one. In the proposed model, the first term measures the fitting error, while the second term incorporates the structural information of graphs and total variations of time sequence, and hence the model can extract both temporal and spatial information. To illustrate the performance of the proposed model, we analyzed the simulated datasets for epidemic diseases and the real datasets for COVID-19 and mortality rate in mainland China. The results show that the proposed model can capture the trends/regions simultaneously in both temporal and spatial domains, being an effective model to analyze the problems that can be modelled as time-varying graphs.