Using the first-principles calculation combined with the structure searching method, the ternary intermetallic compound (IMC) (Ni0.66, Zn0.33)3Sn4 with $R\bar 3m$ space group is predicted. The energetic, dynamic, thermal, and mechanical stabilities of the (Ni0.66, Zn0.33)3Sn4 IMC are confirmed. The mechanical, thermodynamic, and electronic characteristics at different pressures from 0 to 20 Gpa for the (Ni0.66, Zn0.33)3Sn4 IMC are also investigated. The results show that the (Ni0.66, Zn0.33)3Sn4 IMC possesses a ductile trait within 20 Gpa and that pressurization can increase its elastic modulus, hardness, anisotropy, Debye temperature, and minimum thermal conductivity. At a given pressure, the thermal expansion coefficient α increases significantly below 200 K, and then its increase rate approaches a linear mode as the temperature increases. Compared with the case of 0 GPa, the shapes of the total density of states and partial density of states for the (Ni0.66, Zn0.33)3Sn4 IMC change slightly at pressure 20 Gpa, implying that its structure is still stable under pressure 20 GPa.