The 1960 Copa del Generalísimo Juvenil was the tenth staging of the tournament. The competition began on May 15, 1960, and ended on June 26, 1960, with the final.
First round
| Team 1 | Agg. | Team 2 | 1st leg | 2nd leg |
|---|---|---|---|---|
| Zaragoza | 4–2 | Atlético Madrid | 3–0 | 1–2 |
| Elizondo | 8–0 | Mirandés | 3–0 | 5–0 |
| Laredo | 3–4 | Firestone | 3–0 | 0–4 |
| Badajoz | 3–4 | Valladolid | 2–3 | 1–1 |
| Murcia | 5–4 | Valencia | 5–2 | 0–2 |
| Ciutadella | 3–8 | Badalona | 1–3 | 2–5 |
| Celta de Vigo | 4–1 | La Braña | 2–0 | 2–1 |
| Betis | w/o | Ceuta | 3–1 | – |
Quarterfinals
| Team 1 | Agg. | Team 2 | 1st leg | 2nd leg |
|---|---|---|---|---|
| Zaragoza | 4–6 | Elizondo | 3–3 | 1–3 |
| Celta de Vigo | 1–4 | Firestone | 1–1 | 0–3 |
| Valladolid | 5–2 | Betis | 2–2 | 3–0 |
| Murcia | 7–5 | Badalona | 5–2 | 2–3 |
Semifinals
| Team 1 | Agg. | Team 2 | 1st leg | 2nd leg |
|---|---|---|---|---|
| Elizondo | 3–4 | Firestone | 1–2 | 2–2 |
| Valladolid | 2–4 | Murcia | 2–0 | 0–4 |
Final
| Team 1 | Score | Team 2 |
|---|---|---|
| Firestone | 5–2 | Murcia |
| Copa del Generalísimo Winners |
|---|
| Firestone |