This letter introduces a novel wireless-powered backscatter communication system which allows sensors to utilize RF signals transmitted from a dedicated RF energy source to transmit data. In the proposed system, when the RF energy source transmits RF signals, the sensors are able to backscatter the RF signals to transmit date to the gateway and/or harvest energy from the RF signals for their operations. By integrating backscattering and energy harvesting techniques, we can optimize the network throughput of the system. In particular, we first formulate the time scheduling problem for the system, and then propose an optimal solution using convex optimization to maximize the overall network throughput. Numerical results show a significant throughput gain achieved by our proposed design over two other baseline schemes.