A simple CSMA-based random access scheme to improve broadcast reliability is proposed in this letter. We consider successful delivery probability as a broadcast reliability measure. Hinted from the result on the optimal access probability in the slotted-Aloha, the access probability in a-persistent CSMA is designed to improve the successful delivery probability. An analytical model is also presented to evaluate the performance of the proposed scheme. The results show that the proposed scheme significantly improves the successful delivery probability of broadcast messages, in comparison with the existing ones.