A walking beam pumping system is disclosed wherein the pumping system's prime mover is gravity. In one embodiment, the system comprises a walking beam pivotally coupled to a support structure at a pivot point substantially central along the length of the walking beam. A counterbalance weight is disposed along the length of the walking beam. A position device is provided for moving the counterbalance weight along at least a portion of the length of the walking beam. As the counterbalance weight moves along the length of the walking beam, the beam's center of gravity is modulated. By modulating the position of the counterbalance weight in an appropriate manner, the walking beam is caused to pivot back and forth with respect to the support structure. A pumping assembly, for example a sucker rod string, is attached to one end of the walking beam, such that as the walking beam pivots back and forth, the pumping system is actuated to pump fluid out of, for example, an oil well bore. In one embodiment, the positioning device for moving the counterbalance weight comprises a linear motor.