The core-shell structure precipitatates of Fe-xCu-3.0Mn-1.5Ni-1.5Al alloys under internal and external strain was investigated by using a multicomponent continuous phase field model based on Gibbs free energy of sub regular solution. Results show that the early cluster nuclei are not pure Cu, and Mn/Ni/Al also gather in the same position of Cu rich nuclei, resulting in four core-shell structures in precipitation. In the absence of external strain, the morphology of precipitates is mainly determined by interfacial energy, intrinsic elastic anisotropy and lattice distortion between new phase and parent phase. Intrinsic elastic strain energy can inhibit precipitation, while has no obvious effect on particle morphology. In coarsening, the elastic energy decreases due to the combination of particles. The loading direction and magnitude of the applied elastic strain field can control the morphology of precipitates. The external strain and the interaction between Mn, Ni and Al promote the joining and merging of adjacent core-shell particles. This work has guiding significance for the design of Fe-xCu-3.0Mn-1.5Ni-1.5Al alloys and other core-shell precipitates materials.