In this paper, we consider an energy harvesting cognitive radio sensor network (EH-CRSN), which is composed of multiple secondary users (sensor nodes) opportunistically access licensed channels. We first propose a novel single-sink EH-CRSN and derive its network throughput. Then, we extend the EH-CRSN to the multi-sink case which will cause interference among secondary communications. To deal with this problem, we optimize channel access schedule, so as to maximize the network throughput in many actual large-scale scenarios. Specifically, we formulate a mixed interaction game and demonstrated the existence of Nash equilibrium. A stochastic learning automata (SLA)-based channel selecting an algorithm is further proposed to achieve the Nash equilibrium. Finally, the simulation results verify the validity of network throughput function in single-sink EH-CRSN and show that the proposed solution can get the maximum or near-maximum system throughput.