Required:

- Pokémon 1 that knows Sleep Powder
- Pokémon 2 that knows Disable
- Pokemon 3 Diglet lvl 15 in that order
- 5 Pokéballs (any type, except masterball)
- Space left for Abra (Pc or Party).

Save you're game data, and look for Abra on route 24.
Use sleep powder without fail. and next use Disable without fail too. and next Diglet. use scratch and Abra's Hp will catch by a half. Throw a Ball to catch him, make sure you have 5 Pokéballs or less.
By any chase, if Abra use Teleport you'll have to start over.

Note: Abra is also easy to catch with a Masterball, but if you play fairly, you can use the method above.