To alleviate the spectrum scarcity problem, exploiting the vast available spectrum provided by the Millimeter-Wave (mmWave) frequency band and underlaying cellular network by Device-to-Device (D2D) communication are two promising solutions. In this paper, we focus on D2D-underlaid cellular network, where the D2D communication is performed on a hybrid manner (i.e., operating over either mmWave or microwave frequency band). To secure the hybrid D2D communication against vigilant adversary, we apply covert communication to hide its presence. In particular, the D2D transmitters perform power control and communication mode switch as well as leveraging the cellular signal to avoid the transmission detection by the adversaries. We model the conflict between the D2D transmitters and adversaries in the framework of a two-stage Stackelberg game. The D2D transmitters are the leaders to maximize their utility subject to the constraints on communication covertness at the upper stage. The adversaries are the followers to minimize their detection errors at the lower stage. We apply stochastic geometry to mathematically characterize the network spatial configuration and consider a large-scale D2D-underlaid network, enabling the study from system-level perspective. We analyze the game equilibrium and obtain it by adopting a bi-level algorithm. Numerical results are provided and insightful conclusions are drawn. Compared with the conventional D2D communication, hybrid D2D communication shows a significant advantage regarding throughput under the same security requirement while weak resistance to the more stringent security requirement.