A system of a concrete floor and a concrete floor levelling device, wherein the concrete floor comprises a floor reinforcement having reinforcement profiles, which have a mutual spacing; and concrete, which has been poured over the floor reinforcement and is still fluid or viscous. The concrete floor levelling device comprises a blade carriage suitable for, during use, being moved in a direction of travel over the concrete floor, so that the still fluid or viscous concrete behind the blade carriage is levelled by the concrete levelling device; and a levelling blade coupled with the blade carriage such that, during use, the levelling blade is kept at a defined height on the concrete floor, whereby the concrete floor is levelled by the levelling blade. The blade carriage is provided with at least one wheel set, which is/are constructed and arranged to each bear a therewith associated part of the blade carriage on a reinforcement profile transversely to the direction of travel. Each wheel set comprises at least two wheels, each having its own rotation axis, which rotation axes are displaced with respect to each other over a spacing in a direction transversely to the rotation axes and parallel to the direction of travel of the concrete levelling device. The spacing between the rotation axes is unequal to the spacing between the reinforcement profiles or a multiple thereof.