A balance beam game apparatus includes at least a base and at least a combining piece. A surface of the combining piece is an arc-shaped surface and another surface of the combining piece is a horizontal plane. Two ends of the combining piece are provided respectively with a locking slot at a proper location, a connecting slot is disposed above and below the base respectively, and the connecting slot can be latched with the combining piece. A wall on each of two sides of the connecting slot is provided respectively with a locking block which can be selectively latched in the locking slot of the combining piece. Therefore, by combining the abovementioned elements, a game apparatus in all kinds of combinatorial change in routes can be formed.