Unlike terrestrial communication, underwater acoustic communication utilizes sound waves. The sound speed is dependent on the water temperature and the salinity. The sound transmission path is changed by refraction according to the gradient of vertical sound velocity. When sound waves are passed through the underwater, they are affected by attenuation, reflection of bottom and surface, scattering, ambient noise, and the Doppler effect caused by movement of the transmitter and the receiver. Even due to the doppler effect, the received signal is expanded and compressed. Sometimes it is necessary to hide and protect our information from stranger. However, due to the characteristics of underwater acoustic communication using sound waves, the probability of detection is higher than that of terrestrial communication, and our information is easily intercepted. Therefore, it is necessary to study on the covert communication along with the reliable communication in the underwater acoustic channel. In this thesis, a covert underwater acoustic communication method that is robust to fading using a chirp signal combined with a frequency-hopping spread spectrum scheme is designed and demodulated to new type receiver. A fractional Fourier transform (FrFT), which estimates the slope of the signal frequency variation, is applied to the receiver to enable a robust and reliable symbol estimation with respect to the frequency and irregular phase variations. Using FrFT, the chirp signal can be distinguished and other frequencies can be treated as noise. Therefore, FrFT receiver is a different demodulation method compared to conventional correlator receiver. In addition, since the recursive symbol synchronization can be implemented using a chirp signal, compression and expansion effects due to the Doppler shift can be mitigated. Simulation and lake trials were performed to verify the performance of the proposed method.