Abstract The middle-aged Galactic supernova remnant (SNR) the Cygnus Loop (CL) displays a peculiar morphology in X-rays, featuring a blowout in the southern region. The underlying process accounting for the formation of the peculiar periphery remains a mystery. To this end, we conduct hydrodynamical simulations to investigate the SNR evolution coupled with a tailored stellar-wind model: a bipolar stellar wind emanating from a runaway red supergiant progenitor, excavating a wind-blown cavity elongated along the $-z$-direction. Our simulation results reveal that the forward shock of the consequent SNR sweeps up the modified ambient media, shaping the overall morphology with a blowout comparable to that of CL. Besides, a series of simulation runs are performed to assess the impacts of different model parameters and the projection effect (observational angle $\theta_{\mathrm{obs}}$) on the final SNR profile. Three physical quantities are extracted from simulation results to characterize the simulated SNR and make a direct comparison with the X-ray observations of CL. We find that the final SNR morphology is sensitive to both stellar-wind properties and $\theta_{\mathrm{obs}}$. A Cygnus-Loop-like SNR could be reproduced under appropriate parameter combinations at $\theta_{\mathrm{obs}}=0^{\circ}$. While for $\theta_{\mathrm{obs}}\lesssim30^{\circ}$, the projected morphology akin to CL could be also generated under specific conditions.