The Follow-up X-ray Telescope (FXT), a key payload onboard the Einstein Probe sallite (EP), is equipped with a Wolter-I x-ray focusing mirror system. We introduce the principle of such a mirror system and analyze the influence of the mirror gap in the multishell nested mirror of the FXT on the effective area, stray-light ratio, and vignetting. To ensure that no occlusion occurs within adjacent shells and minimize stray-light ratio, the size of the gap is set to a optimized value for corresponding shell. We finished a design of a 54-shell mirror system according to these results. The optical performance of the design was then simulated using a Monte Carlo algorithm and the ray-tracing principle. The simulation shows that the effective area is 414.5  ±  0.2  cm² at 1.25 keV (considering the spider), and the field of view is 64 arcmin in diameter. These parameters meet the optical requirements of the FXT.