Traditional local-earthquake location using a horizontally layered homogeneous velocity model is limited in its resolution and reliability due to the existence of frequently overlooked 3D complexity of the real Earth. During traditional 3D seismic tomography, simultaneous earthquake relocation using the resultant 3D velocity model has produced reliable earthquake locations; however, only a small subset of events are typically used and thus relocated in the inversion. The rest of the events in a catalog must then be relocated using the 3D models. The repeated calculation of travel times across 3D VP and VS models is also not efficient and not practical for a routine network earthquake location when the very time-consuming exact 3D raytracing is used. Because high-resolution earthquake data are now available from many modern seismic networks, representative high-resolution 3D VP and VS models for a region can be better determined. By taking advantage of recently available high-speed computer technology and large disk space, we implemented a simple algorithm to efficiently locate every local earthquake using the best available regional 3D VP and VS models. Once the VP and VS information for all cubic cells in a 3D grid model are determined, P and S travel times from each grid point to all seismic stations can be calculated and stored on disk files for later usage. During the iteration process for earthquake location, travel times from a trial hypocenter to all recording stations can be determined simply by a linear interpolation from those of the adjacent eight grid points available in the previously stored disk files without the need for raytracing. The iterations continue until the hypocenter adjustments at the end of the last iteration are below the given criteria and the travel-time residual, or the difference between the observed and the calculated travel times, is a minimum. Therefore, any local earthquake can be efficiently and reliably located using the available 3D velocity models. This simple location program has been applied to relocate earthquakes in the New Madrid Seismic Zone (nmsz) of the central United States and in the central eastern Taiwan region. Preliminary results in both regions reveal that earthquake hypocenters can be efficiently relocated in spite of the very significant lateral structural variations. Tests with data from Taiwan further demonstrate that the resolution of seismic tomography and the relocated seismicity is sensitive to relative distribution of seismic-network stations and background seismicity. Thus, this single-event location program can be applied to relocate all earthquakes in a seismic-network catalog and, more importantly, to allow routine earthquake location for any seismic network using the available 3D velocity models.