The invention discloses a real-time calculation and monitoring method of bridge stay cable force and a monitoring alarm system. The monitoring method comprises the steps that firstly, vibration signals of the inhaul cable are collected in real time through collecting equipment of the monitoring alarm system, then the monitoring equipment of the monitoring alarm system calculates the real-time inhaul cable force according to the vibration signals, finally whether the inhaul cable force exceeds a preset warning threshold value or not is judged, and if yes, the monitoring equipment sends out an alarm signal. The inhaul cable force calculation method comprises the steps that firstly, monitoring equipment obtains a vibration signal of an inhaul cable, and secondly, Hilbert-Huang transform method is adopted to perform time-frequency domain transformation on the vibration signal to obtain vibration frequency time history data, and finally a real-time stay cable force is calculated according to the vibration frequency time history data.