Gunn made six full international appearances for Scotland, conceding 10 goals. He was a member of the squad for the 1990 FIFA World Cup, but played in none of Scotland's three matches at the tournament, as he was third-choice goalkeeper behind Jim Leighton and Andy Goram. He made his Scotland debut in a pre-tournament friendly match against Egypt, but was at fault for two Egyptian goals, resulting in a 3–1 defeat for Scotland. The embarrassment was made worse by the fact that his parents were watching. Gunn made four appearances for Scotland in 1994 FIFA World Cup qualification matches. His last cap was as a second-half substitute in a 3–1 friendly defeat by the Netherlands in May 1994.