The soft exosuit is a new approach for applying assistive forces over the wearer's body through load paths configured by the textile architecture. In this paper, we present a body-worn lower-extremity soft exosuit and a new control approach that can independently control the level of assistance that is provided during negative- and positive-power periods at the ankle. The exosuit was designed to create load paths assisting ankle plantarflexion and hip flexion, and the actuation system transmits forces from the motors to the suit via Bowden cables. A load cell and two gyro sensors per leg are used to measure real-time data, and the controller performs position control of the cable on a step-by-step basis with respect to the power delivered to the wearer's ankle by controlling two force parameters, the pretension and the active force. Human subjects testing results demonstrate that the controller is capable of modulating the amount of power delivered to the ankle joint. Also, significant reductions in metabolic rate (11%-15%) were observed, which indicates the potential of the proposed control approach to provide benefit to the wearer during walking.