A hybrid technique combining the Pseudo-Spectral Time-Domain method with the Finite-Volume Time-Domain method is presented to solve 3-D mixed-scale problems, which contain both electrically large and relatively homogeneous regions and electrically small fine details in computational electromagnetics. FVTD is suitable for electrically small problem but suffers from large numerical errors for electrically large-scale regions. The PSTD method, on the other hand, is accurate and efficient for regions with large and relatively homogeneous materials, but is low in efficiency for electrically small structures. The hybrid method overcomes disadvantages and unites advantages of either method mentioned and is potentially more useful. A least square based quadratic polynomial reconstruction method is developed for FVTD to reduce the reflection brought by the boundary of the algorithms, then an overlapping grids scheme and a no overlapping grids scheme are presented. Numerical examples demonstrate that the method proposed enjoys high level of precision and strong capability in region analysis.