In this research work we have modeled a single gate SOI MOSFET using high dielectric gate material HfO2 instead of as usual low dielectric gate material SiO2, Dielectric constant of SiO2 is 3.9 whereas HfO2 has a value of 26 which is almost seven times (exactly 6.67) on comparison to SiO2 gate material. Also the energy gap of HfO2 is 5.65 eV. We have considered a long channel SOI MOSFET and Poisson's equation is solved carefully along the depth of the channel. The gradual channel approximation (GCA) technique has been considered for solving the 1-D Poisson's equation. Dependency of the surface potential with the gate biases is shown mathematically in our paper. Beside this insulating layer of HfO2 shows several beneficial advantages like— (i) lowering the leakage current, (ii) lowering the threshold voltage and (iii) ideal sub threshold behavior.