Future fusion reactors such as ITER have adopted tungsten (W) as the plasma-facing materials (PFMs) in the divertor region. It is crucial to keep the W concentration in the core plasma at an extremely low level. Great efforts have been put forward on understanding the W transport in the scrape-off layer (SOL), which is related to the source of the core W contamination. In this work, the influence of E×B drift on the W impurity transport in the SOL is studied by numerical simulations for a model case based on EAST upper single-null configuration with high recycling divertor plasma. The W transport is simulated using DIVIMP on the background plasma obtained from SOLPS-ITER simulation including drifts. The E×B drift of the W ions is introduced according to the background electric field. Therefore, both the direct E×B drift effect of W ion itself and the indirect effect via background plasma on the W transport process in the SOL can be studied. We focus on the influence on the flux of W impurities entering confined plasma across the last closed flux surface Γenter, which is expected to be proportional to the core W concentration. It is found that Γenter is mainly from the outer (inner) target under favorable (unfavorable) toroidal field BT, and can be increased by more than one order of magnitude compared with the case without drifts. It reflects the significant influence of E×B drift effects. The detailed effects due to the background plasma and the poloidal and radial E×B drift of W ion, as well as the related mechanisms, are analyzed for the three stages of W transport in the SOL, including the effective sputtering from the target, the leakage from the divertor and the entry into the confined plasma.