As a fundamental magnetic structure in the solar corona, electric current sheets (CSs) can form either prior to or during a solar flare, and they are essential for magnetic energy dissipation in the solar corona because they enable magnetic reconnection. However, the static reconstruction of a CS is rare, possibly due to limitations that are inherent in the available coronal field extrapolation codes. Here we present the reconstruction of a large-scale preflare CS in solar active region. 11967 using an MHD-relaxation model constrained by the SDO/HMI vector magnetogram. The CS is associated with a set of peculiar homologous flares that exhibit unique X-shaped ribbons and loops occurring in a quadrupolar magnetic configuration. This is evidenced by an 'X' shape, formed from the field lines traced from the CS to the photosphere. This nearly reproduces the shape of the observed flare ribbons, suggesting that the flare is a product of the dissipation of the CS via reconnection. The CS forms in a hyperbolic flux tube, which is an intersection of two quasi-separatrix layers. The recurrence of the X-shaped flares might be attributed to the repetitive formation and dissipation of the CS, as driven by the photospheric footpoint motions. These results demonstrate the power of a data-constrained MHD model in reproducing a CS in the corona as well as providing insight into the magnetic mechanism of solar flares.