Earlier in the day the pilot had discovered a minor engine oil leak in his airplane. The leak was fixed by a certificated airframe and power plant mechanic and the pilot then changed the airplane's oil. The pilot stated that the purpose of the flight was to make sure that the oil leak was repaired. He flew one circuit in the traffic pattern and landed normally. The pilot reported that he had full control of the airplane until he applied the brakes. According to the pilot, he "applied [the brakes] a little too soon," and the airplane veered to the right and exited the runway. In the grass on the side of the runway, the airplane momentarily nosed down and the propeller touched the ground. The airplane then settled back down normally with the engine stopped. The airplane sustained substantial damage to the left wing and main wing spar. The pilot reported no mechanical malfunction or failure with the airplane prior to the accident.