In this paper, a novel underwater unidirectional acoustic transmission (UAT) device consisting of a plate with bilateral asymmetric gratings is proposed and numerically investigated. The transmission spectra, the acoustic intensity field distributions, and the displacement field distributions are numerically calculated based on the finite element method. The transmission spectra show that the proposed device exhibits different UAT effects in three bands. The acoustic intensity field distributions demonstrate that the proposed device can realize UAT, which agree well with the transmission spectra. The mechanism is discussed by analyzing the displacement field distributions, and the UAT is attributed to the symmetric mode excited in brass plate. Furthermore, the effects of the lattice constant, the upper slit width, and the lower slit width on bands are discussed. Our design provides a good reference for designing underwater UAT devices and has potential applications in some fields, such as medical ultrasonic devices, acoustic barrier, and noise insulation.