The structural, mechanical, electronic, dynamic, and optical properties of the ZrPdSn compound crystallising into the MgAgAs structure are investigated by the ab initio calculations based on the density functional theory. The lattice constant, bulk modulus, and first derivative of bulk modulus were obtained by fitting the calculated total energy-atomic volume results to the Murnaghan equation of state. These results were compared to the previous data. The band structure and corresponding density of states (DOS) were also calculated and discussed. The elastic properties were calculated by using the stress-strain method, which shows that the MgAgAs phase of this compound is mechanically stable. The presented phonon dispersion curves and one-phonon DOS confirms that this compound is dynamically stable. In addition, the heat capacity, entropy, and free energy of ZrPdSn were calculated by using the phonon frequencies. Finally, the optical properties, such as dielectric function, reflectivity function, extinction coefficient, refractive index, and energy loss spectrum, were obtained under different pressures.