First Round
17-Sep-63 FC Basle Sui 1-5 Celtic Sco (Celtic Goals Divers, Hughes 3, Lennox)
10-Oct-63 Celtic Sco 5-0 Basle Sui (Celtic Goals Johnstone, Divers 2, Murdoch, Chalmers)
agg Celtic 10-1 Basle


Second Round
04-Sep-63 Celtic Sco 3-0 NK Dinamo (Zagreb) Yug (Celtic Goals Chalmers 2, Hughes)
11-Sep-63 Dinamo (Zagreb) Yug 2-1 Celtic Sco (Celtic Goal Murdoch)
agg Celtic 4-2 Dinamo Zagreb


Quarter-Finals
16-Feb-64 Celtic Sco 1-0 Slovan Bratislava Tch (Celtic Goal Murdoch pen)
04-Mar-64 Slovan Bratislava Tch 0-1 Celtic Sco (Celtic Goal Hughes)
agg Celtic 2-0 Slovan Bratislava

Semi-Finals
Olympique Lyonnais Fra Sporting CP (Lisbon) Por 0-0 1-1 1-1 [0-1]x
15-Apr-64 Celtic Sco 3-0 MTK (Budapest) Hun (Celtic Goals Johnstone, Chalmers 2)
29-Apr-64 MTK (Budapest) Hun 4-0 Celtic Sco
agg Celtic 3-4 MTK Budapest