The Cu-rich phase is a high-efficiency and ultra-stable precipitation-strengthening phase and has been widely used in many steels and alloys, especially in heat-resistant steels and alloys. Creep damage is accompanied with the coarsening of the second phase. In the present work, the calculation of phase diagrams (CALPHAD) method and elastic–plastic mechanics are coupled with the phase field (PF) approach to investigate the growth behavior and the accompanying stress/strain field evolution of nano-sized Cu-rich precipitates in an Fe-Cr-Ni-Cu medium-entropy alloy. The results show that creep strain is intensified with the coarsening of Cu-rich particles. The simulated size of Cu-rich particles is in good agreement previous experimental reports. The plastic strain tends to shear the Cu-rich phase when they are relatively fine (~<11 nm), and the size of the Cu-rich particles has a slight influence on the creep strain at this stage. In contrast, coarse Cu-rich precipitates (~>11 nm) are bypassed by the plastic strain due to the enhancing stress concentration around the interface, and the creep strain is rapidly aggravated with the growth of Cu-rich particles. The coarsening of Cu-rich particles will be retarded by the adjacent particles due to the overlapping of the diffusion zone, and hence the creep strain was reduced when crept for the same time. The retard effect will vanish when their distance is sufficiently long (~>60 nm). When the size of the Cu-rich particles is identical, the creep strain will be mitigated with elongation of the distance between two Cu-rich particles.