Dynamic spectrum access (DSA) has drawn immediate attention recently since it can opportunistically exploit any spectrum holes and thus improve bandwidth utilization. From the perspective of medium access control (MAC) design, the QoS requirement of SU is one of the design issues in DSA network. In this paper, we propose a new admission control scheme referred to as log-based dynamic spectrum access admission control (DSAC) aiming at (1) protection of the primary users and (2) QoS prioritization for the existing secondary users. The DSAC algorithm protects the PU by limiting SUs' access using PU's arrival log or statistics. Furthermore, the DSAC reserves a channel for previously admitted SU to reduce frequent service disruption of the SU. Reservation of channels is carried out without assuming any specific arrival process, and thus the DSAC would be practical for general user arrival patterns unlike the existing admission control techniques. Performance evaluation has shown that the proposed DSAC outperforms existing admission control schemes with respect to the PU blocking rate, SU communication stability, and SU aggregate throughput by about 13%, 26%, and 20%, respectively.