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Backscatter communication has recently emerged as a promising technology to enable the passive sensing-based Internet-of-things (IoT) applications. In a backscatter communication network, uplink transmissions of multiple nodes are usually multiplexed in time- or frequency-domain to avoid collisions, yet it is desirable to improve the uplink capacity further. In this paper, we study a wireless-powered backscatter communication system, where the sensors use a hybrid channel access scheme by combining time division multiplexing access (TDMA) with power-domain non-orthogonal multiple access (PD-NOMA) to enhance the system performance in terms of outage probability and throughput. Our analysis shows that the proposed PD-NOMA increases both the spectrum efficiency and the throughput of the system.