We develop a system, which enables an early warning of earthquake occurrence several seconds before large ground shaking begins. We assume that the vertical displacement of the broadband P waveform can be considered as the far-field source time function of the earthquake. Based upon the seismic moment to source duration relation, we may issue an early warning that an earthquake with magnitude greater than 6 has occurred, when the initial P-wave pulse duration continues for more than 3 seconds. We have applied this algorithm to broadband seismograms recorded at Japanese broadband stations for recent large earthquakes in Japan. We found that it really is possible to assess the occurrence of earthquakes with magnitude greater than 6 within 3 seconds after the P-wave arrival.