is a town in Merrimack County, New Hampshire, United States. The population was 4,843 at the 2000 census. Allenstown includes a portion of the village of Suncook. Just over one-half of the town's area is covered by Bear Brook State Park.
Allenstown takes its name from 17th-century provincial governor Samuel Allen. It was granted in 1721 but not incorporated until 1831. A part of Allenstown was lost to Bow in 1815, and another part to Hooksett in 1853.