The relationship among the on-to-off current ratio, threshold voltage, and the gate metal work-function is investigated for a junctionless (JL) Gate-All-Around (GAA) MOSFET with a gate oxide film in which SiO2 and a high-k dielectric material are stacked. The JL structure works in the accumulation state, and the threshold voltage is defined as the gate voltage when the minimum potential in the channel becomes Fermi potential. The on-to-off current ratio Ion/Ioff is obtained by obtaining on-current Ion at the threshold voltage and off-current Ioff at the gate voltage of 0 V. As a result, if the channel doping concentration and silicon radius are increased to reduce the channel resistance, the on-to-off current ratio decreases along with the threshold voltage, but this problem can be solved through the increasing of the gate metal workfunction. In addition, even when the relative permittivity of the high-k dielectric is increased from 3.9 to 20, the gate metal work-function to maintain any on-to-off current ratio and threshold voltage is very slightly changed. Therefore it will be possible to improve the controllability of the gate by increasing the permittivity of the high-k dielectric without change in the work-function. The reduction of the channel resistance of the JL GAA MOSFET is possible with the stacked gate oxide while maintaining a reasonable on-to-off current ratio and threshold voltage by adjusting the gate metal work-function