A milking device is provided with milking device, a control unit, a milk line for transporting the milk from the milking device to a milk tank, a milk filter for filtering the milk passing through the milk line, and a cleaning device for the milk filter with cleaning liquid. The milk filter includes a housing surrounding a filter volume and has a milk inlet and a milk outlet, and a filter component in the filter volume. The filter component includes a circumferential plate part with filter holes, and divides the filter volume into a central inner filter volume and an outer filter volume surrounding the latter. The milk filter is configured to be flushed, in use, with the milk to be filtered from the milk inlet to the milk outlet. The cleaning device is configured to clean the milk filter by passing cleaning liquid through the milk filter in a countercurrent direction in consecutive pulses, in such a way that, in each pulse, during a first pulse stage more cleaning liquid is supplied than is discharged, and subsequently, during a second pulse stage, at least as much cleaning liquid flows from the filter volume as is supplied. As a result thereof, an amount of cleaning liquid always collects in the filter volume up to a liquid level, which surrounds at least some of the plurality of holes. The next pulse makes cleaning liquid collide with the liquid level, which improves the cleaning of the filter.