Antiphase boundaries (APBs) of L12 ordered γ′-Co3 (Al, W) precipitates have an essential effect on the high-temperature strength of Co-based monocrystal superalloys. In this work, the antiphase boundaries and their effects on the evolution kinetics of γ′ phase are studied with the phase-field model. The formation of APBs between γ′ phases with different crystallographic variants induces a sharp increase in free energy; the width of APBs measured by the edge-to-edge distances of the γ′ phase is consistent with the experimental results of superalloys. Also, a coupling behavior of Ostwald ripening and APB’s migration in the coarsening of the γ′ phase is revealed. In addition, the volume fraction of the γ′ phase with four antiphase domains is lower than that of the single-domain γ′ phase, and the time exponent of the particles’ number density of the γ′ phase at the steady coarsening stage changes from –0.99 of single domain to –0.8 of APBs. The results show that the high-energy APBs can reduce the coarsening rate of γ′ phases, which are significant in the microstructure and composition designing of the ordered precipitates with APBs in Co-based superalloys.