Written and first recorded by Johnny Smith (1954).
Also recorded by Chet Atkins (1957).
Hit versions by The Ventures (US #2/R&B #13/UK #8 1960), The John Barry Seven (UK #11 1960), The Ventures (as “Walk, Don’t Run ’64” US #8 1964).
From the wiki: “‘Walk, Don’t Run’ is an instrumental composition written and first recorded by jazz guitarist Johnny Smith in 1954. In 1957, Chet Atkins recorded a version of ‘Walk, Don’t Run’ that appeared on his Hi-Fi in Focus album.
“It was the Atkins recording the Tacoma-based instrumental rock band The Ventures heard before releasing their own version of the tune as a Surf Rock single in spring 1960 on Dolton Records, which quickly became a hit. The Ventures’ version is believed to be one of the first surfing songs to make the Billboard Hot 100 chart, peaking at #2. In the UK, the tune was covered by The John Barry Seven (before Barry began scoring movie music for the likes of James Bond, Born Free, and Midnight Cowboy) whose cover of the Ventures’ arrangement peaked at #11 on the UK Singles Chart.”