| Pos. | Driver | Entrant | Constructor | Time | Grid |
|---|---|---|---|---|---|
| 1 | Jim Clark | Team Lotus | Lotus-Climax | 57:39.0 | 2 |
| 2 | Peter Arundell | Team Lotus | Lotus-Climax | + 1:21.6 | 4 |
| 3 | Trevor Taylor | British Racing Partnership | Lotus-BRM | 41 laps | 8 |
| 4 | Richard Attwood | Owen Racing Organisation | BRM | 41 laps | 9 |
| 5 | Mike Hailwood | Reg Parnell Racing | Lotus-BRM | 40 laps | 16 |
| 6 | André Pilette | Equipe Scirocco Belge | Scirocco-Climax | 37 laps | 15 |
| 7 | John Taylor | Gerard Racing | Cooper-Ford | 37 laps | 11 |
| 8 | Peter Revson | Revson Racing (America) | Lotus-BRM | 35 laps | 13 |
| 9 | Giancarlo Baghetti | Scuderia Centro Sud | BRM | 35 laps | 10 |
| Ret | Graham Hill | Owen Racing Organisation | BRM | Rotor arm | 3 |
| Ret | Jo Bonnier | Rob Walker Racing Team | Cooper-Climax | Accident | 7 |
| Ret | Bernard Collomb | Bernard Collomb | Lotus-Climax | Accident | 14 |
| Ret | Ian Raby | Ian Raby (Racing) | Brabham-BRM | Ignition | 12 |
| Ret | Jack Brabham | Brabham Racing Organisation | Brabham-Climax | Wheel rim | 1 |
| Ret | Innes Ireland | British Racing Partnership | BRP-BRM | Accident | 5 |
| Ret | Bruce McLaren | Cooper Car Company | Cooper-Climax | Accident | 6 |
| WD | Phil Hill | Cooper Car Company | Cooper-Climax | - | |
| WD | Chris Amon | Reg Parnell Racing | Lotus-BRM | - | |
| WD | André Wicky | André Wicky | Lotus-BRM | - |
Date: 30 March 1964
Official Name: I News of the World Trophy
Circuit: Goodwood Circuit
Location: West Sussex
Circuit Length: 3.862 km
Number of Laps: 42
Race Distance: 162.2 km
Pole Position: Jack Brabham, Brabham-Climax, 1:21.0
Fastest Lap: Graham Hill, BRM, 1:21.0