The most recent was Lyndon B. Johnson (1969), but in total he served 6 years because he took over the presidency when Kennedy was assassinated, so I don't know if that counts.
Truman (1953) and Coolidge (1929) were essentially in the same boat (were officially first term presidents who did not seek reelection, even though they had already served more than 4 years due to their predecessor dying).
You have to go back to Rutherford B Hayes (1881) for a true, 4 year president who did not seek reelection.