An efficient, robust and fully automatic grid assembly method on multi-block cell-centered structured grids for massively parallel computation is proposed in this paper. Compared with the traditional serial algorithm, the new approach eliminates the complex irregular boundaries created during the grid partition and avoids the large load imbalance caused by the large variation of grid-block overlapping. The main task of the overlapping grid assembly is to categorize all grid points into field points, fringe points and hole points. As to the main processes of the overlapping grid assembly, for hole cutting, an improved hole map method is applied to accurately identify the hole points located on the wall boundary with less memory cost. For donor search which is the most complex process on account of the irregular distribution of the partitioned multi-block structured grids in a parallel computation environment, the Alternating Digital Tree (ADT) is utilized to find out the potential donor cells quickly for query points. Besides, to achieve better overlapping quality, the wall distance criterion is implemented for overlapping optimization. In addition, two load balance algorithms are designed to solve the imbalance problem of overlapping grid assembly. Two test cases are applied to test the new overlapping grid assembly algorithm and the results show that the new overlapping grid assembly algorithm can deal with large-scale simulation of vehicles. The comparison of total time and speed-up among three algorithms manifests that the initial load balance algorithm using query point number as load criterion is not reliable while the improved load balance algorithm achieves good speed-up and least runtime. Meanwhile, the maximum proportion the improved load balance algorithm takes in one physical unsteady step in wing-pylon-store separation test case is less than 6.1%.