The use of high-capacity motors and harmonic drives increases the manufacturing cost and the energy consumption of the robot. It is well known that most motor torques are used to support the robot mass and payload. To deal with this problem, we propose a wall-mounted 3-DOF roll-pitch-pitch counterbalance mechanism (CBM). Unlike previous CBMs used for floor-mounted industrial robot arms, the proposed CBM can be applied to wall-mounted robots in which the first three joints are all coupled and affected by gravity. This mechanism is composed of pure mechanical components such as coil springs, differential gear structure, and belt-pulley system. A 6-DOF robot arm equipped with the proposed CBM was fabricated to verify the performance of gravity compensation. It is shown that the proposed 3-DOF CBM can effectively compensate for gravitational torques, thus drastically reducing the motor torques required to operate the robot.