Covertness is playing an increasingly important role in underwater acoustic communication (UAC). However, traditional underwater acoustic communication signals with specified characteristics cannot ensure the concealment of the communication signal. To solve the problem, a bionic covert UAC scheme based on dolphin whistle with time-delay, abbreviated as BCUAC-TD, is proposed in this paper. In the proposed BCUAC-TD scheme, we divide the time-frequency structure (TFS) into several segments uniformly to represent different symbol signals, and the time-delay is used to carry different information. Moreover, the energy compensation and the virtual time reversal mirror (VTRM) are adopted to improve the performance the demodulation. The performance of proposed BCUAC-TD scheme is evaluated by simulations under simulated and experimental channels, and the covertness and effectiveness of proposed covert communication scheme are verified.