Teleseismograms play an important role in global seismology. Because most earthquakes occur in the regions with active tectonics, which have complex structures and therefore cause strong 3D effects in teleseismograms. Numerical simulations of wave propagation are able to accurately model these 3D effects. However, simulations of high frequency (e.g. 1 Hz or higher) wave propagation at the global scale is still prohibitive due to the limited computation capability. To overcome this difficulty, we proposed a hybrid method to efficiently compute teleseismic waveforms with 3-D source-side structures. By coupling the Spectral Element Method (SEM) with the Direct Solution Method (DSM) based on the representation theorem, we are able to limit the costly SEM simulation to a small source-side region and avoid computation over the entire space of the Earth. Our hybrid method reduces computational cost by more than two orders of magnitude when only source-side 3-D complexities are of concern. We have successfully used this hybrid method to investigate a series of problems in seismology, such as imaging 3-D structures of a subducting slab and studying source parameters with 3-D source-side complexities.