MAC protocols to sense channels for data transmission have been widely investigated for the secondary users to efficiently utilize and share the spectrum licensed by the primary user. One important issue associated with MAC protocols design is how the secondary users determine when and which channel they should sense and access without causing harmful interference to the primary user. In this paper, we jointly consider the MAC-layer spectrum sensing and channel access. Normal Spectrum Sensing (NSS) is required to be carried out at the beginning of each frame to determine whether the channel is idle. On detecting the available transmission opportunity, the secondary users employ CSMA for channel contention. The novelty is that, Fast Spectrum Sensing (FSS) is inserted after channel contention to promptly detect the return of the primary users. This is unlike most other MAC protocols which do not incorporate FSS. Having FSS, the primary user can benefit from more protection. A concrete protocol design is provided in this paper, and the throughput-collision tradeoff and utility-collision tradeoff problems are formulated to evaluate its performance. Simulation results demonstrate the efficiency of the proposed MAC protocol with FSS.