The circuit simulation model Hiroshima-university STARC IGFET Model silicon-on-insulator (HiSIM-SOI) for the fully depleted SOI metal-oxide-semiconductor field-effect-transistor (MOSFET) is developed based on the surafce-potential description. To include all device features of the SOI-MOSFET explicitly, the surface potential values not only at the SOI surface but also the back side, as well as the bulk back-gate are solved iteratively. The total iteration for the potential calculation requires only about twice as much calculation time as the bulk-MOSFET case, solving ony at the surface. The model reproduces measured I-V characteristics within numerical accuracy, and is proved stable circuit convergence.