As one of the most fundamental properties of wireless networks, latency is important to the information dissemination, routing protocol design and node deployment. Different from the traditional wireless network, the spectrum resource in cognitive radio networks is dynamic which affects the network latency drastically. Thus, how to analyze the latency of large-scale cognitive radio networks under the dynamic spectrum environments is a challenging problem. To address this problem, this paper first constructs a dynamic spectrum environment model in which the process of the licensed spectrum access is defined as a continuous-time Markov chain, and a survival function of secondary users is created to quantify the impact of the number of channels and the activities of primary users. Next, this paper combines the proposed model with the first passage percolation theory to investigate scaling laws of latency in large scale cognitive radio networks. It also derives a tighter upper bound of the ratio of latency to distance. Theoretical analysis and simulation results show that the dynamic spectrum environments have a great impact on the latency of large-scale cognitive radio networks as well as the density. The results provide important guidelines for the design of cognitive radio networks.