A lawn mower having a deck height adjustment mechanism for simultaneously adjusting a height of a deck of a lawn mower at all four wheels of the lawn mower by the use of a single hand of the operator. The mechanism includes an index plate having a plurality of teeth thereon defining a plurality of deck height positions, and therefore a plurality of height positions of a cutting blade supported by the deck. The index plate is fixedly secured to an offset rear axle. An engaging plate having a pawl is coupled to an actuating member which is slidably, vertically moveable relative to the deck when the operator grips the actuating member and pulls upwardly away from the deck, while resting a palm of the same hand on a palm rest portion of the mechanism. A linkage member couples the index plate to a bracket of an offset front axle positioned at a front end of the deck. The operator adjusts the height of the deck relative to a ground surface by pulling upwardly with the fingers of one hand on the actuating member, while resting the palm of the same hand on the palm rest. This causes the engaging plate, and thus the pawl thereon, to be drawn out of engagement with the teeth of the index plate. The operator, while holding the actuating member engaged, may either pull upwardly with the same hand, thus raising the entire deck of the mower, or may urge the deck into a lower position. Movement of the index plate causes a simultaneous rotational movement of the offset front axle. Thus, all four corners of the deck are caused to be raised or lowered simultaneously as the operator either lifts or lowers the deck while engaging the actuation member.