McNear was born in Los Angeles to Luzetta M. Spencer and Franklin E. McNear. He studied at the Oatman School of Theater and later joined a stock company in San Diego. McNear also worked in radio from the late 1930s, distinguishing himself in the 1937–1940 radio serial Speed Gibson of the International Secret Police as ace operator Clint Barlow. McNear could be effective in such authoritative roles, but he gravitated more toward character roles, often comic.As "Doc" in the Gunsmoke radio cast
He created the role of Doc Charles Adams in CBS Radio's Gunsmoke (1952–1961). McNear was under contract to CBS for many years and was featured in many of the network's radio and TV programs. From 1955 to 1960 he appeared frequently, in various quirky roles, in the popular radio detective series Yours Truly, Johnny Dollar.
McNear made his film debut in an uncredited role in the 1953 film Escape from Fort Bravo. Over the course of his career, he would appear in over 100 film and television guest spots. In 1958, McNear guest starred as a barber named Andy on an episode of Leave It to Beaver, a role which proved prophetic. In 1961, he was cast as the vague, chatty barber Floyd Lawson on The Andy Griffith Show. During the show's run, McNear suffered a stroke that rendered the left side of his body nearly paralyzed. McNear left the series for nearly a year and a half to recover. Andy Griffith later asked McNear to return to the series. McNear agreed but was unable to walk or stand. The production crew accommodated his disability and McNear was usually seen seated or standing with the support of a stand. According to Jack Dodson (who playedHoward Sprague on Andy Griffith), McNear began having difficulty remembering his lines and became anxious and frustrated. He left the series in 1967.