pilotart is correct, the airfield at Midway was built by the U.S. military in 1941. That first airstrip was built on Eastern Island, not on Sand Island (the bigger of the two islands forming Midway Atoll). The current airfield at Midway is on Sand Island. It is mostly abandoned/dormant, used very rarely as an emergency landing field for some trans-Pacific airliner having mechanical difficulties.
See the book "A Glorious Page in Our History: The Battle of Midway, 4-6 June 1942". The first part of this book includes a short history of Midway prior to WW II.
Bruce Thomas -- The airstrip on Midway was not named Henderson Field. Henderson Field was constructed later on Guadacanal. Henderson Field was named in honor of USMC Major Lofton Henderson, who was killed in action, flying from the Midway airstrip, during the Battle of Midway.
Jeff P.