A four-dimensional ensemble-variational (4DEnVar) data assimilation (DA) system was developed for global numerical weather predictions (NWPs). 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) initialized from its previous inflated analyses and realizes the flow-dependence of BEC in the variational configuration during the assimilation cycle. These inflated analyses, linear combinations of the ensemble analyses increment and balanced random perturbations, aim to prevent the predicted BEC from underestimation as well as to implicitly achieve the hybrid of the flow-dependent and static BEC matrices. A limited number of leading eigenvectors of the localization correlation function are selected to filter out the spurious correlations in the BEC matrix (B-matrix). 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. The flow-dependent characteristic was verified in the SOEs that utilized the localized ensemble covariance and compared with that of 4DVar. In the OSSEs, 4DEnVar reduced the analysis errors compared with 4DVar. The deterministic forecast initialized from the 4DEnVar ensemble mean analysis has better (worse) performance in the medium-range (long-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 from the 4DEnVar ensemble analyses has higher forecast skills than 4DVar.