This paper considers a single-hop wireless network where a fusion center (FC) collects data from a set of m energy harvesting (EH) sensors. In each time slot, k of m nodes can be scheduled by the FC for transmission over k communication channels. FC has no knowledge about the EH processes and current battery states of sensors; however, it knows the outcomes of previous transmission attempts. Also, battery leakage is ignored since it is very small. The objective is to find a low complexity scheduling policy that maximizes the total throughput of the data backlogged system for general case of EH process in finite or infinite horizon. A low-complexity and near optimal policy UROP (Uniformizing Random Ordered Policy) is proposed for a general case of EH process under infinite battery assumption. Simulations indicate that under a reasonable-sized finite battery assumption, there is almost no loss in throughput.