A new Elementary Modified Levenberg–Marquardt Algorithm (M-LMA) was used to minimise backpropagation errors in training a backpropagation neural network (BPNN) to predict the records related to the Chi-Chi earthquake from four seismic stations, Station-TAP003, Station-TAP005, Station-TCU084 and Station-TCU078, with the learning rates of 0.3, 0.05, 0.2 and 0.28, respectively. For these four recording stations, the M-LMA has been shown to produce smaller predicted errors compared to LMA. A sudden predicted error could be an indicator for Early Earthquake Warning (EEW), which indicated the initiation of strong motion due to large earthquakes. a trade-off decision-making process with BPNN (TDPB), using two alarms, adjusted the threshold of the magnitude of predicted error without a mistaken alarm. This approach was not necessary to consider the problems of characterising the wave phases and pre-processing, but did not require complex hardware; an existing seismic monitoring network-covered researched area was already sufficient for these purposes.