A four‐dimensional ensemble‐variational (4DEnVar) data assimilation (DA) system was developed based on the global forecast system of the Global/Regional Assimilation and Prediction System (GRAPES‐GFS). Instead of using the adjoint technique, this system utilizes a dimension‐reduced projection (DRP) technique to minimize the cost function of the standard four‐dimensional variational (4DVar) DA. It dynamically predicts ensemble background error covariance (BEC) and realizes the explicit flow‐dependence of BEC in the variational configuration. An inflation technique based on a linear combination of analysis increments and balanced random perturbations, is utilized to overcome the problem of underestimation of BEC matrix (B‐matrix) during the assimilation cycle. To mitigate the spurious correlations in the ensemble B‐matrix caused by the insufficient ensemble members, an ensemble‐sample‐based subspace localization method is utilized. In order to evaluate the new system, single‐point observation experiments (SOEs) and observing system simulation experiments (OSSEs) were conducted with sounding and cloud‐derived wind data based on GRAPES‐GFS. The explicit flow‐dependent characteristic of the 4DEnVar system using a localized ensemble covariance was verified in the SOEs. In the OSSEs, the ensemble mean analysis of 4DEnVar outperforms the analysis of 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better performance in the short‐range forecasts, better (worse) performance in the early (late) period of the medium‐range forecasts in the Northern Extratropics, and opposite performance in the Southern Extratropics, and exhibits slightly worse effects in the Tropics. Moreover, the ensemble mean forecast initialized by the 4DEnVar system has higher forecast skills. Plain Language Summary: Medium‐range numerical weather prediction aims to predict weather states for future 1–10 days from the current state by solving the initial value problem of a set of partial differential equations. Data assimilation (DA) is one of the key techniques to improve forecast skills, which attempts to provide an optimal estimation of the current state by combining observations and forecasts. This study developed a four‐dimensional ensemble‐variational (4DEnVar) DA system based on the global forecast system of the Global/Regional Assimilation and Prediction System (GRAPES‐GFS) applying the dimension‐reduced projection (DRP) four‐dimensional variational (4DVar) approach. Compared with the standard 4DVar, which is generally recognized as one of the most advanced DA methods, this new system has three unique features. First, it dynamically estimates background error covariance (BEC) during the assimilation cycle instead of adopting a pre‐estimated static BEC as 4DVar does. Second, it uses a pure anisotropic ensemble covariance. Third, it can avoid using adjoint models and handle nonlinear problems well. The observing system simulation experiments based on GRAPES‐GFS verify that 4DEnVar has smaller analysis errors, and better ensemble mean forecast skills than 4DVar, and comparable skills of deterministic forecast initialized from the ensemble mean analysis to 4DVar. Key Points: A DRP‐4DVar based 4DEnVar data assimilation system with the flow‐dependent background error covariance was developed for global numerical weather predictionThe deterministic forecast initialized from the 4DEnVar ensemble mean analysis has performance comparable to 4DVar in the ExtratropicsHigher quality of analyses and ensemble forecasts can be produced by the 4DEnVar system relative to the 4DVar system [ABSTRACT FROM AUTHOR]