Ferroelectricity and weak ferromagnetism have been found to set in simultaneously in Ni3B7O13I at ∼64°K. This is evidenced by dielectric hysteresis, spontaneous Faraday effect, quadratic magnetoelectric hysteresis, etc. The strong coupling between the mutually perpendicular spontaneous polarization--[001]--and spontaneous magnetization--[110]--is such that, when the former is reversed, the latter turns by 90°. The magnetic point group is most probably m'm2'. Dielectric constant, magnetic, and magnetoelectric susceptibilities and magnetic coercive field are shown as a function of temperature.