This paper uses the C++ to develop an adapted band matrix solver to simulate the i-v curve and the drain current of the 2-D double-gate n-channel MOSFET, including different doping concentrations which from 5×10 (cm -3) to 5×10 (cm-3) and channel thickness which from 5 nm to 15 nm. And it discusses the threshold voltage from the i-vg curve and selects the more appropriate doping concentration and channel thickness to complete the following experiments. And then it simulates if-vg curve to determine threshold voltage which can present the channel on-off situation and calculates drain current which is in different gate voltage. It also can simulate the electric potential of the x-axis and y-axis. In the figure of the electric potential we can obtain the depletion width. It also analyzes the subthreshold, the linear and the saturation region in i-v curve, and we can find out the values of sub-threshold swing in the subthreshold region of the i-v curve and the value of the drain current in the saturation region of the i-v curve. It compares the results with the other reference papers. Finally, the equations of the threshold voltage can be developed, and we calculate the threshold voltage of double-gate n-channel MOSFET. The result obtained by the equation of the threshold voltage will be compared with result by 2-D simulation. The depletion width can be obtained as an analytical equation. The analytical depletion width can be verified by the figure of the x-axis and y-axis electric potential from 2-D simulation. The 2-D simulation also verifies the result with the drain current equation which is obtained by Pois-son's equation. For circuit application, an inverter including a double-gate n-channel MOSFET and a 100kΩ resistor will be used to simulate the v o-vi characteristics and analyzes the parameters of the inverter (e.g. VOh, VOl, Vih, Vil, VS), and the noise margin (e.g. NML, NMH) will be calculated in order to determine the inverter's performance and quality.