Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting systems. Despite the significant successes that have been achieved (e.g., surpassing advanced traditional physical models for global medium-range forecasting), existing data-driven weather forecasting models still rely on the analysis fields generated by the traditional assimilation and forecasting system, which hampers the significance of data-driven weather forecasting models regarding both computational cost and forecasting accuracy. In this work, we explore the possibility of coupling the data-driven weather forecasting model with data assimilation by integrating the global AI weather forecasting model, FengWu, with one of the most popular assimilation algorithms, Four-Dimensional Variational (4DVar) assimilation, and develop an AI-based cyclic weather forecasting system, FengWu-4DVar. FengWu-4DVar can incorporate observational data into the data-driven weather forecasting model and consider the temporal evolution of atmospheric dynamics to obtain accurate analysis fields for making predictions in a cycling manner without the help of physical models. Owning to the auto-differentiation ability of deep learning models, FengWu-4DVar eliminates the need of developing the cumbersome adjoint model, which is usually required in the traditional implementation of the 4DVar algorithm. Experiments on the simulated observational dataset demonstrate that FengWu-4DVar is capable of generating reasonable analysis fields for making accurate and efficient iterative predictions.