According to the pilot, while in the process of executing a terminal instrument approach to his home airport, he transitioned from instrument meteorological conditions (IMC) to visual meteorological conditions (VMC). He therefore canceled his instrument flight rules (IFR) clearance, and transitioned from the terminal instrument approach to a visual flight rules (VFR) approach pattern. During this sequence of events, the pilot, who was not following a written checklist, inadvertently forgot to lower the landing gear. During the landing flare, the pilot heard the noise caused by the wing flaps and both propellers contacting the surface of the runway, and therefore he added power and immediately executed a go-around. The pilot then entered a closed pattern, lowered the landing gear and repositioned the flaps, before making an uneventful landing. According to the pilot, during his approach he heard the gear warning horn sounding, but he thought it was the altitude alerting system. An inspection of both the runway surface scarring and each propeller blade revealed that the tips of all six blades had been ground down by repeated contact with the asphalt surface. The pilot also said that the airplane did not have any system malfunctions.