Mew does not appear anywhere in the wild in "Pokémon Leaf Green," meaning it is impossible to catch him. It is possible to obtain a Mew through certain other methods. The best way is to use either an Action Replay or a Game Shark. These are devices that allow the player to activate certain cheats in the game that make all Pokémon available to be captured.
Players can use an Action Replay or Game Shark code on their Game Boy that makes any Pokémon available to be caught in the wild in "Pokémon Leaf Green." They can also give themselves an infinite supply of Master Balls; that way they will have a 100 percent chance of capturing Mew.
If you wish to obtain a Mew that appears to have been caught legitimately then you must use your Action Replay or Game Shark in the game "Pokémon Emerald." Then you must find and use a cheat that gives the player the Old Sea Map item. Using this item, it is possible to obtain a Mew that will seem legitimate. Then that Mew can be traded from "Pokémon Emerald" into "Pokémon Leaf Green."
The Mew from the Old Sea Map item cheat generates a Mew into the game that appears to have been caught legitimately because there was once an event in Japan that gave players the Old Sea Map and then let them capture a Mew.