This paper investigates a wireless-powered communication network (WPCN) setup with one multi-antenna access point (AP) and one single-antenna source. It is assumed that the AP is connected to an external power supply, while the source does not have an embedded energy supply. But the source could harvest energy from radio frequency (RF) signals sent by the AP and store it for future information transmission. We develop a discrete time-switching (DTS) protocol for the considered WPCN. In the proposed protocol, either energy harvesting (EH) or information transmission (IT) operation is performed during each transmission block. Specifically, based on the channel state information (CSI) between source and AP, the source can determine the minimum energy required for an outage-free IT operation. If the residual energy of the source is sufficient, the source will start the IT phase. Otherwise, EH phase is invoked and the source accumulates the harvested energy. To characterize the performance of the proposed protocol, we adopt a discrete Markov chain (MC) to model the energy accumulation process at the source battery. A closed-form expression for the average throughput of the DTS protocol is derived. Numerical results validate our theoretical analysis and show that the proposed DTS protocol considerably outperforms the existing harvest-then-transmit protocol when the battery capacity at the source is large.