A common method to examine the current-limiting performance of saturated iron-core fault current limiter (SI-FCL) in high-voltage direct-current transmission based on voltage source converter (VSC-HVDC) systems is to solve differential equations based on the system fault transient characteristics and the equivalent inductance calculation equation. This method analyzes the fault current of the VSC-HVDC system in the time domain. However, it is computationally complex and cannot directly reflect the relationship between parameters and the currentlimiting effect of the SI-FCL. In this paper, the relationship between the magnetic flux density and magnetic field energy of the SI-FCL is analyzed. The energy exchange between the DC capacitor and the SI-FCL in the DC short circuit fault process is analyzed. From the perspective of electromagnetic energy conversion, the criterion for determining the current-limiting ability of the SI-FCL in the transient process is given based on the parameters of the SI-FCL and VSC-HVDC system. On this basis, the characteristics of the DC side fault current and the capacitor voltage when the SI-FCL has current-limiting ability are examined. Based on the parameters of the SI-FCL and VSC-HVDC system, a method for calculating the fault current peak value and capacitor voltage drop time is given. Finally, the accuracy of the analysis of the SI-FCL in the VSC-HVDC system based on the electromagnetic energy conversion mechanism is demonstrated through a case study and simulation results of the VSC-HVDC system with different SI-FCLs.