We have developed a new method for the simultaneous determination of the earthquake source parameters: seismic moment, focal mechanism, rupture length, and rupture velocity, using far-field P-waves. The pseudo radiation patterns of P-waves are obtained from each station, accomplished through a grid search of the source time function and simple inversion. The observed waveforms are corrected for instrument response, geometrical spreading and surface effects. These corrections are made for the corresponding ray parameter of each station based on IASP91 velocity model. To obtain the best solution for the focal mechanism, pseudo radiation patterns are compared with the theoretical radiation patterns calculated for the given focal mechanisms obtained through the grid search. The source time functions obtained from all available stations for an earthquake are used to estimate the rupture length and rupture velocity based on rupture directivity. We have applied this method to three moderate- to large-sized global earthquakes. The results agree well with those of previous studies, suggesting that this method is applicable for seismic hazard assessment. A moderate Taiwan earthquake is analyzed to demonstrate that the method can indeed be used to rapidly determine the source parameters of earthquakes in Taiwan.