A pump device for a motor vehicle includes: a pump having a first pump member and a second pump member, the first and second pump members being movable relative to one another; an electric drive having a drive housing and an output shaft rotatable with respect to the drive housing; and a gear mechanism, which couples the output shaft to the first pump member and, by reversing a direction of rotation of the electric drive, is switchable between a first and an opposite second transmission ratio. The gear mechanism has: a planet stage having a planet carrier rotationally fixed relative to the drive housing, and/or first and second freewheels, oppositely directed with respect to one another, and which are arranged axially behind one another, and/or the second pump member has a drive shaft rotatable relative to the output shaft.