To provide a liquid ejection head cleaning device capable of surely cleaning an ejection face of a liquid ejection head, and to provide an inkjet recorder and a method of cleaning a liquid ejection head.

The liquid ejection head cleaning device includes a wiping member for wiping an ejection face of a liquid ejection head constituted of a face of a nozzle member having a nozzle row and a projection face having a step portion with respect to the face of the nozzle member, and a plurality of pressing means that press the wiping member to bring it into contact with the ejection face of the liquid ejection head that relatively moves. Sizes of pressing widths of the plurality of pressing means in a direction perpendicular to a moving direction of the liquid ejection head are different from one another.