A hand-held electronic game machine includes a computer accommodated in a case and a liquid crystal display (LCD) panel provided at an upper portion of a front surface of the case. When an external memory is inserted to a receiving port formed on a rear surface of the case at a portion opposite to the LCD panel, a first character data being set in advance in the computer is compared with a second character data stored in a predetermined area of the external memory. Prior to such comparison, the computer displays the characters represented by the second character data on the LCD panel. If the first and second character data are coincident with each other, the computer can access to the external memory. During the progression of the game in accordance with a game program of the external memory, the game character can be moved by operating a direction designating key provided at the left side in a portion below the LCD panel of the front surface of the case, and the action manner of the game character can be determined by operating an action key provided at the right side in the portion below the LCD panel. A start key and select key are arranged between the direction designating key and the action key.