The threshold voltage (Vth) variability in fully depleted SOI MOSFETs with intrinsic channel and ultrathin buried oxide under back bias voltage (Vbs) is extensively investigated by three dimensional device simulation. It is found that the Vth variability increases only slightly by applying negative Vbs by the effect of random dopant fluctuation (RDF) in the substrate, while the Vth variability is severely degraded by applying positive Vbs by the effect of the back interface inversion. As a result, there is a certain value of Vbs around 0 V where the Vth variability is minimized.