In this paper, the problem of dynamic pricing over multiple rounds of spectrum leasing is investigated. One primary network is considered, which is the spectrum seller that would like to lease its unused channels to secondary users. To accommodate different arrival instants of secondary users' spectrum requests, spectrum leasing is performed in multiple rounds (stages), and in each stage, a separate spectrum price is set. First, we consider the case that, for each specific price value, the spectrum demand (the number of channels requested by secondary users) is a random variable. An optimization problem is formulated to set up the spectrum prices in the multiple stages, with the purpose of maximizing the total revenue of the primary network. The solving method of the formulated optimization problem is presented. Additionally, some interesting properties of the optimal solution are also presented, such as monotonicity and convexity of the maximal total revenue with respect to the stage index and lower/upper bounds of the maximal total revenue. Furthermore, we consider the case that, for a specific price value, the spectrum demand is nonrandom and can be solely determined by the price. An incremental algorithm is given to find out the optimal price values at the stages. We also demonstrate the monotonicity of the optimal price value with respect to the stage index. Numerical results are provided to verify the research findings and compare them with existing work.