Moving the torso laterally in a walking biped robot can be mechanically more torque-efficient than not moving the torso according to recent research. Motivated by this observation, a torque-efficient torso-moving balance control strategy of a walking biped robot subject to a persistent continuous external force is suggested and verified in this paper. The torso-moving balance control strategy consists of a preliminary step and two additional steps. The preliminary step (disturbance detection) is to perceive the application of an external force by a safety boundary of zero moment point, detected approximately from cheap pressure sensors. Step 1 utilizes center of gravity (COG) Jacobian, centroidal momentum matrix and linear quadratic problem calculation to shift the zero moment point to the center of the support polygon. Step 2 makes use of H-infinity controllers for a more stable state shift from single support phase to double support phase. By comparing the suggested torso moving control strategy to the original control strategy that we suggested previously, a mixed balance control strategy is suggested. The strategy is verified through numerical simulation results.