We propose an efficient Hermite spectral method for the spatially non-homogeneous Fokker-Planck-Landau (FPL) equation. We split the FPL equation into three parts, which are the convection step, the acceleration step and the collision step. Two different expansion centers are employed in the Hermite spectral method, among which the standard one used in [R. Li, Y. Wang, and Y. Wang. SISC. 2020] is selected during the convection and collision step in order to utilize the expansion coefficients of the quadratic collision term calculated therein and the one constituted by the local macroscopic velocity and temperature is selected for the acceleration step, by which the effect of the external force can be simplified into a system of ODE. The transformations between distribution functions with different expansion centers are achieved by a highly efficient algorithm [24]. In order to further reduce the complexity of the quadratic FPL collision term, a novel collision model is designed with a combination of the quadratic collision term and the simplified collision term. Several numerical examples are studied to test and validate our new approach.