Palladium hydrides (Pd-H) research is an important topic in materials research with many practical industrial applications. The complex behavior of the Pd-H alloy system such as phase miscibility gap, however, presents a huge challenge for developing reliable computational models. The embedded atom method (EAM) offers an advantage of computational efficiency and being suited to the metal-hydride system. We propose a new EAM interatomic potential for the complete mathematical modeling of palladium hydride. The present interatomic potential well predicts the lattice constant, cohesive energy, bulk modulus, other elastic constants, and stable alloy crystal structures during molecular dynamics simulations. The phase miscibility gap is also accurately predicted for the Pd-H system using the present potential. To our knowledge, only two Pd-H EAM potentials were used for predicting the phase miscibility gap for the PdH system. The predicted values from these works, however, considerably deviated from the experimental result, which hinders further application to the palladium hydride system. The present potential is reliably accurate and can be used to study the Pd-H system with its compete description of the mathematical formalism.