The early tsunami monitoring system relies mainly on seismic monitoring network or subsea manometer array network. However, these methods all have the problems such as high cost of construction and maintenance and limited monitoring scope, and so on. From actual observations and numerical simulations of tsunami, it has been found that the widely distributed subsea cables can reflect the induction electromagnetic field produced by the movement of tsunami, from which more convenient and economical methods for monitoring the tsunami-induced electromagnetic field (TIEF) are developed. The theoretical derivation process of the TIEF is introduced and the analytical solutions of the TIEF under the cases of different tsunami velocity models and seafloor topographical types are studied. By comparing the merits and faults of monitoring the voltage, disturbance magnetic field and vector electromagnetic field of TIEF, it is found that the monitoring of the vector electromagnetic field has the advantage of measuring the propagation direction of tsunami and the application of the vector electromagnetic field monitoring together with the existing tsunami monitoring system can make the warning of tsunami faster, more accurate and more real time.