After shakedown off Cuba, Glennon sailed from Boston, Massachusetts on 12 February 1946 for Europe and visited many of the nations washed by the North Sea before returning to New York in August of the same year.

Sailing from Norfolk, Virginia in June 1948, Glennon served with the Midshipman Practice Squadron and made calls at Portugal, Italy, and French Morocco.

In the winter of 1949–50 she was part of "Operation Frostbite", a cold weather exercise near the Davis Strait, subsequently to sail from Newport on 4 January 1950 for another "Med" cruise.

Glennon spent January and February 1952 with a carrier task force conducting cold weather training in waters ranging northward to the Davis Straits.

Highlights of this exacting duty included participation as a recovery station ship in the 1961 and 1962 Project Mercury flights, and in the search for the lost nuclear powered submarine Thresher (SSN-593).

In August 1961 Glennon was called away suddenly to join the task force for the Project Mercury space shot carrying Major Gus Grissom.