Teleseismic wave adjoint tomography is able to image the deep structure of the lithosphere. Here we proposed the element-by-element spectral-element method (EBE-SEM) for efficient teleseismic wave modeling. A detailed discussion of the teleseismic seismic incident boundary condition and PML absorbing boundary condition for the scattered waves are presented. Beside the high efficiency of EBE-SEM for the forward modeling of teleseismic waves, it is able to easily construct misfit kernels.