At about 1100 central time, a Cessna 172N collided with a fence during the landing roll at a private airstrip at Circle Bar Ranch. The pilot and passenger were not injured. The pilot said he overflew the airstrip and observed the windsock, which indicated the wind was from the northeast at approximately 10 knots. He entered the traffic pattern for runway 09, and twice performed a go-around. Following the second approach, the wind was from the northwest and he entered the traffic pattern for a full-stop landing on runway 27. He touched down about a quarter of the way down the 2,400-foot runway but, at the midpoint of the runway, the airplane accelerated, apparently due to a wind shift. The airplane would not stop before the end of the runway, so he intentionally maneuvered the airplane off the left side of the runway. A witness said the airplane touched down about midpoint of the runway. Examination revealed the airplane left the runway about 204 feet before the end of the pavement and then traveled 492 feet.