Several approaches for fast generation of digital holograms of a three-dimensional (3D) object have been discussed. Among them, the novel look-up table (N-LUT) method is analyzed to dramatically reduce the number of pre-calculated fringe patterns required for computation of digital holograms of a 3D object by employing a new concept of principal fringe patterns, so that problems of computational complexity and huge memory size of the conventional ray-tracing and look-up table methods have been considerably alleviated. Meanwhile, as the 3D video images have a lot of temporally or spatially redundant data in their inter- and intra-frames, computation time of the 3D video holograms could be also reduced just by removing these redundant data. Thus, a couple of computational methods for generation of 3D video holograms by combined use of the N-LUT method and data compression algorithms are also presented and discussed. Some experimental results finally reveal that by using this approach a great reduction of computation time of 3D video holograms could be achieved.