In this paper, the distributed channel access schemes for ALOHA-based cognitive radio networks are considered. In the considered system, time is divided into frames, which are further divided into sensing phase and transmission phase. We derive channel sensing policy in the sensing phase, and channel access policy in the transmission phase for a secondary user (SU) to maximize its throughput. To mitigate high complexities of the above scheme, we propose a threshold-based channel access scheme. In this scheme, an appropriate threshold is set based on channel occupancy information and channel state information, and only channels providing potentially high throughput will be sensed and accessed. The proposed schemes are fully distributed, i.e., no extra information exchange is needed among SUs, which is a highly desired and beneficial property. Simulation results confirm that the proposed schemes outperform prior random access schemes.