The cognitive radio slotted-ALOHA (CR S-ALOHA) network is a CR system that consists of two or more secondary users (SUs) utilizing S-ALOHA as the channel access technique. In the CR S-ALOHA network, a sequence of transmission failures can implicate the possibility of primary user (PU) appearance as well as the consecutive collisions between SUs. By exploiting this property, we design a combined channel access and sensing scheme for CR S-ALOHA networks, with which both packet transmission and channel sensing can be controlled together. We analyze the performance of the proposed scheme by formulating a 5-D Markov chain. The numerical results show that the CR S-ALOHA network with the proposed scheme achieves good performance in throughput and delay while protecting the PU properly.