An improved swimming pool cleaner of the type for submerged random travel generally along the floor and sidewalls of a swimming pool to dislodge and collect debris. The pool cleaner comprises a frame and associated housing through which a suction mast extends with a collection bag mounted at the upper end thereof. First and second wheels are mounted for rotation on a common axis on opposite sides of the housing forwardly of the suction mast, and third and fourth wheels are mounted for rotation on a common axis on opposite sides of the housing rearwardly of the suction mast. The first and second wheels are driven by a water-powered drive train within the housing, and the third and fourth wheels are mounted for freewheeling rotation. A forward end of an upper surface of the housing has a substantially linear sloping portion to reduce the tendency of the cleaner to lift off the submerged surfaces of the swimming pool as the first and second wheels propel the cleaner in the forward direction.