An extension of the density-gradient model to include the non-local transport effect is presented. The governing equations can be derived from the first three moments of the Wigner distribution function with some approximations. A new nonlinear discretization scheme is applied to the model to reduce the discretization error. We also developed a new boundary condition for the $Si/SiO_2$ interface that includes the electron wavefunction penetration into the oxide to obtain more accurate C-V characteristics. We report the simulation results of a 25-nm metal-oxide-semiconductor field-effect transistor (MOSFET) device.