In this paper, we investigate a single-hop wireless sensor network in which a fusion center (FC) collects data packets from M energy harvesting (EH) sensor nodes. Energy harvested by each node is stored without battery overflow and leakage at that node. The FC schedules K nodes over its mutually orthogonal channels to receive data from them in each time slot. The FC knows neither the statistics of EH processes nor the battery states of nodes. The FC solely has information on consequences of previous transmission attempts. We aim for obtaining an efficient and simple policy achieving maximum throughput in this network. The nodes are data backlogged and the data transmission only depends on the harvested energy of the scheduled nodes. A node can transmit data whenever it is scheduled, provided that it has sufficient energy. We propose a simple policy, uniforming random ordered policy (UROP), for the problem. We exhibit that the UROP is nearly throughput-optimal over finite time horizons for a broad class of EH processes. We also prove that for general EH processes, UROP achieves asymptotically optimal throughput over the infinite time horizon under infinite capacity battery assumption. Numerical results indicate that even with finite-capacity batteries, UROP achieves near-optimal throughput over finite time horizons. We believe that UROP is applicable to much wider area than EH wireless sensor networks.