Data-driven weather forecasting models are developing rapidly, but they rely on the initial states (i.e., analysis states) that are typically generated by traditional data assimilation algorithms. Four-dimensional variational assimilation (4DVar) is one of the most widely adopted data assimilation algorithms among numerical weather prediction centers; it is accurate but computationally expensive. In this paper, we aim to couple the AI forecasting model, FengWu, with the 4DVar to build a self-contained data-driven global weather forecasting framework, FengWu-4DVar. To achieve this, we propose an AI-embedded 4DVar algorithm, which consists of three components: (1) a 4DVar objective function embedded with the FengWu forecasting model and its error representation for improving efficiency and accuracy; (2) a spherical-harmonic-transform-based (SHT-based) approximation strategy for capturing horizontal correlation of the background error; (3) an auto-differentiation (AD) scheme for finding the optimal analysis field. Experimental results indicate that, under ERA5 simulated observation data with different proportions and noise, FengWu-4DVar is able to generate accurate analysis fields and has, for the first time, achieved a stable self-contained global weather forecast for an entire year, demonstrating the potential applicability of FengWu-4DVar to real-world scenarios. Moreover, our framework is computationally efficient, about 100 times faster than the traditional 4DVar algorithm under similar experimental settings.