In this study, we find new Ag_yIn_3.33–y/3Se₅ compounds in Ag-In-Se system by static diffusion method combined with common X-ray diffraction and backscattering electron analysis. The crystal structure belongs to the trilateral system with the P3m1 space group, which features a two-dimensional layered structure. The unit cell is composed of 9-atom quantum layers arranged in the sequence of Se1-In1-Se2-In2-Se3-Ag/In3-Se4-In4-Se5, and in-between these layers are bonded by the weak van der Waals force. The sintered bulk samples show highly anisotropic transport properties and have an ultra-low lattice thermal conductivity along the direction parallel to sintering pressure about 0.15 W·m^–1·K^–1 at 873 K. The intrinsically ultra-low lattice thermal conductivity mainly comes from low phonon velocity and the strong coupling between low frequency optical phonon and acoustic phonons. The Ag_yIn_3.33–y/3Se₅ compounds behave as an n-type conduction. The electrical conductivity is 4×10⁴ S·m^–1 and the Seebeck coefficient is –80 μV·K^–1 at room temperature. Therefore, Ag_yIn_3.33–y/3Se₅ compounds show high electrical transport properties in a wide temperature range, and the power factor is around 5 μW·cm^–1·K^–2 in a range of 450–800 K. Owing to the ultra-low lattice thermal conductivity along the direction parallel to sintering pressure, Ag_0.407In_3.198Se₅ reaches a maximum ZT of 1.01 at 873 K and an average ZT of 0.45 at 300–850 K. The discovery of Ag_yIn_3.33–y/3Se₅ expands the n-type copper based chalcogenide and lays an important foundation for the application of copper based chalcogenide.