The airplane overran the runway during rollout. The pilot reported that he thought he was landing at his intended destination airport, which had a 3,000 ft long by 40 ft wide runway. He landed instead at a private, paved airstrip located about 1 to 2 miles from the destination airport. The airstrip runway was oriented the same direction as the destination airport, but was only 1,000 ft long by 20 ft wide. The pilot reported that he had not flown in the area before. Investigation revealed that the FAA had no record of the airstrip, and that it was not noted on charts or in the Airport/Facility Directory. A representative of the airport owner reported that the owner was not aware of any requirement to notify the FAA of the airport. The airstrip was about 7 years old. 14 CFR 157 (FAR Part 157) requires that any person intending to construct or establish a new airport notify the FAA of their intent.