This is an example of the Type M1 protective helmet adopted by the United States military in 1941 to replace the Type M1917. The Type M1 remained as standard issue for almost 45 years until it was replace by the light weight Kevlar Personnel Armor System for Ground Troops Helmet (PASGT) in the mid-1980s.
This particular helmet was worn by Brigadier General Claire Chennault, commander of the 14th Air Force in China during World War II. Chennault is best known for forming the Flying Tigers, a group of American volunteer fighter pilots who flew in support of the Chinese army prior to America's entry into World War II.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.