The 1960 European Nations' Cup quarter-finals was the third round of the qualifying competition for the 1960 European Nations' Cup. It was contested by the eight winners from the round of 16. The winners of each of four home-and-away ties entered the final tournament. The matches were played in 1959 and 1960.
See main article: 1960 European Nations' Cup round of 16.
Each tie winner progressed to the quarter-finals. The quarter-finals were played in two legs on a home-and-away basis. The winners of the quarter-finals would go through to the final tournament.
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The eight matches took place over two legs, taking place in 1959 and 1960. All times are CET (UTC+1).
France won 9–4 on aggregate and qualified for the 1960 European Nations' Cup.----Yugoslavia won 6–3 on aggregate and qualified for the 1960 European Nations' Cup.----Czechoslovakia won 5–0 on aggregate and qualified for the 1960 European Nations' Cup.----Spain refused to travel for the first leg. The Soviet Union qualified for the 1960 European Nations' Cup by walkover.