The ESS Linac will include in total 21 Beam Current Monitors, mostly of ACCT type, to measure the average current over the 2.86 ms beam pulse, the pulse charge and the pulse profile. It is also planned to use a few Fast Current Transformers to check the performance of the fast beam choppers with a rise time as short as 10 ns. In addition to the absolute current measurement, the BCM system needs to measure the differential beam current and act on the Machine Interlock System if the difference exceeds some thresholds. The differential current measurement is particularly important in the low energy part of the Linac, where Beam Loss Monitors cannot reliably detect beam losses. This paper gives an overview of the ESS BCM system and presents some preliminary test results with a commercial ACCT and MTCA.4 electronics.