With the rapid development of wireless communication, the security of wireless transmission has been gaining increasing attention. Because of the openness of wireless signals, legitimate users can be eavesdropped by illegal user. While cognitive radio (CR) provides the benefits on high spectrum efficiency, it also encounters with the problem of secure transmission. In UAV-assisted underlay CR network, we investigate the relationship between the transmission power of secondary network and the secrecy rate of primary user, which conforms to the marginal utility (MU). Therefore, we propose a dynamic transmission power allocation scheme for secondary network based on MU. In order to reduce the influence of MU in CR network, the power splitting ratio between artificial noise (AN) and secondary signal is designed by exponential mode of change. Particularly, we optimize UAV’s position to maximize the secrecy rate of primary user. The formulated problem is very complicated, and a fixed-direction linear search (FLS) algorithm is adopted to solve it. Simulation results show that the proposed scheme can significantly reduce the influence of MU and improve the performance of secure transmission in underlay CR network.