Double-emulsion droplets are usually taken as reactors in micro-fluidics for various applications, such as life science, materials synthesis, and so on, in which a good understanding of the interface behavior of core coalescence is essential but far from being well understood nowadays. In this work, the interface dynamic behavior induced by the core coalescence of a water-in-oil-in-water double-emulsion droplet is numerically investigated. Particularly attention is focused on the effects of droplet diameter and the physical properties of the middle phase because of their key roles. The obtained results indicate that the inner interface deformation of core coalescence results in the outer interface deformation and the degree is determined by the middle-phase resistance. Both the inner and outer interfaces suffer a typical decaying oscillation process, but the outer interface suffers smaller. With increasing viscosity and density of the middle phase, the inner interface deformation coefficient gradually decreases. However, for the outer interface deformation coefficient, it first presents the opposite variation trend; then, the combined effect of the driven force from the inner droplet and the kinetic energy release of the middle phase results in the slight increase of the outer interface deformation coefficient. At last, the expression of the outer interface deformation is obtained. The results of this work will guide the applications involving the core coalescence in the double-emulsion droplet.