Grosvenor was born in Washington, D.C., on November 26, 1901.
 His parents were Gilbert Hovey Grosvenor, the first editor of The National Geographic Magazine, and Elsie May (née Bell) Grosvenor, the daughter of Alexander Graham Bell.
 The year following his birth, he was present at the laying of the cornerstone of the National Geographic Society's first building, Hubbard Hall, while in his grandfather's arms.

In 1919, Grosvenor enrolled in the U.S. Naval Academy.
 On June 8, 1923, he graduated from the Academy with the Class of 1923, which included his lifelong friend, Admiral Arleigh Burke.
Grosvenor was born in Washington, D.C., on November 26, 1901.  His parents were Gilbert Hovey Grosvenor, the first editor of The National Geographic Magazine, and Elsie May (née Bell) Grosvenor, the daughter of Alexander Graham Bell.  The year following his birth, he was present at the laying of the cornerstone of the National Geographic Society's first building, Hubbard Hall, while in his grandfather's arms.
In 1919, Grosvenor enrolled in the U.S. Naval Academy.  On June 8, 1923, he graduated from the Academy with the Class of 1923, which included his lifelong friend, Admiral Arleigh Burke.
Melville Bell Grosvenor