We report a new two-dimensional hexagonal beryllium sulfide (h-BeS) sheet with exceptional properties by extensive first-principles calculations. The h-BeS sheet presents an indirect energy gap of 4.26 eV and an outstanding thermodynamic stability up to 1000 K. Armchair-edged nanoribbons of h-BeS are wide-energy-gap semiconductors with a giant Stark effect, while the zigzag-edged ones are metals with spin glass state. Especially, the ferromagnetic zigzag nanoribbons exhibit a net magnetic moment of nearly 1.15 μ_B. These interesting electronic and magnetic properties suggest the promise of the h-BeS crystal for potential applications and should inspire experimental enthusiasm.