This is a list of singles which reached number-one on the Irish Singles Chart in 1964.
| Issue Date | Song | Artist |
|---|---|---|
| 3 January | "There's Always Me" | Dickie Rock |
| 10 January | ||
| 17 January | ||
| 24 January | ||
| 31 January | "Glad All Over" | The Dave Clark Five |
| 7 February | ||
| 14 February | "Needles and Pins" | The Searchers |
| 21 February | ||
| 28 February | ||
| 6 March | ||
| 13 March | "Bits and Pieces" | The Dave Clark 5 |
| 20 March | "Anyone Who Had a Heart" | Cilla Black |
| 27 March | "I Love You Because" | Jim Reeves |
| 3 April | ||
| 10 April | ||
| 17 April | "Can't Buy Me Love" | The Beatles |
| 24 April | ||
| 1 May | ||
| 8 May | "A World Without Love" | Peter & Gordon |
| 15 May | ||
| 22 May | "Don't Throw Your Love Away" | The Searchers |
| 29 May (joint No. 1) |
"Fallen Star" | Eileen Reid |
| "I'm Yours" | Dickie Rock | |
| 5 June | "My Boy Lollipop" | Millie |
| 12 June | "It's Over" | Roy Orbison |
| 19 June | "My Boy Lollipop" | Millie |
| 26 June | "It's Over" | Roy Orbison |
| 3 July | "Bless You" | Brendan Bowyer |
| 10 July | ||
| 17 July | "It's Over" | Roy Orbison |
| 24 July | "I Won't Forget You" | Jim Reeves |
| 31 July | ||
| 7 August | "A Hard Day's Night" | The Beatles |
| 14 August | ||
| 21 August | ||
| 28 August | "I Won't Forget You" | Jim Reeves |
| 4 September | ||
| 11 September | ||
| 18 September | ||
| 25 September | ||
| 2 October | ||
| 9 October | "I Wouldn't Trade You for the World" | The Bachelors |
| 16 October | "I'm Into Something Good" | Herman's Hermits |
| 23 October | "Oh, Pretty Woman" | Roy Orbison |
| 30 October | "From the Candy Store on the Corner to the Chapel on the Hill" | Dickie Rock |
| 6 November | ||
| 13 November | ||
| 20 November | ||
| 27 November | ||
| 4 December | ||
| 11 December | "Down Came The Rain" | Butch Moore |
| 18 December | "I Feel Fine" | The Beatles |
| 25 December |