One of the fundamental issues in the design of dynamic spectrum access policy is the modeling of the dynamic behavior of channel occupancy by primary users. Under a Markovian modeling of channel occupancy, a periodic sensing and greedy access policy is known as one of the simple and practical dynamic spectrum access policies in cognitive radio networks. In this paper, the primary occupancy of each channel is modeled as a discrete-time alternating renewal process with generally distributed on- and off-periods. A periodic sensing and greedy access policy is constructed based on the general channel occupancy model. Simulation results show that the proposed policy has better throughput than the policies using channel models with exponentially distributed on- or off-periods.