A dual completion linear rod pumping apparatus for imparting reciprocating vertical motion to a pair of rods for respective sucker-rod pumps. The dual completion linear rod pumping apparatus includes first and second linear mechanical actuator systems disposed in a single housing. These linear mechanical actuator systems impart and control vertical motion of the pair of rods. Each linear mechanical actuator system includes a rack and pinion gearing arrangement. The rack is operatively connected in a gear-mesh relationship with the pinion. The pinion is operatively connected to a rotating output of a motor. Rotation of the motor in a first direction results in an upward motion of the rack and connected sucker rod pump. Rotation of the motor in a second direction opposite the first direction results in a downward motion of the rack and connected sucker rod pump. An electronic controller is operatively connected to the motor.