A new hybrid reconstruction scheme DDG/FV is developed in this work by combining the DDG method and DG/FV hybrid scheme developed in the authors' previous work [1–4] to simulate three-dimensional compressible viscous flow on tetrahedral grids. The extended von Neumann stencils are used in the reconstruction process to ensure the linear stability, and the L₂ projection and the least-squares method are adopted to reconstruct higher order distributions for higher accuracy and robustness. In addition, a quadrature-free L₂ projection based on orthogonal basis functions is implemented to improve the efficiency of reconstruction. Three typical test cases, including the 3D Couette flow, laminar flows over an analytical 3D body of revolution and over a sphere, are simulated to validate the accuracy and efficiency of DDG/FV method. The numerical results demonstrate that the DDG scheme can accelerate the convergence history compared with widely-used BR2 scheme. More attractively, the new DDG/FV hybrid method can deliver the same accuracy as BR2-DG method with more than 2 times of efficiency improvement in solving 3D Navier-Stokes equations on tetrahedral grids, and even one-order of magnitude faster in some cases, which shows good potential in future realistic applications.