The flexible interconnection controller (FIC) is a type of power electronic device based on Insulated Gate Bipolar Transistors (IGBT) modules, which is applied to electrical distribution systems to realize the flexible control of power flow. The reliability of this device plays an important role in the reliable and continuous operation of the active distribution system. In this paper, a reliability model of FIC which consists of three modular multilevel converters (MMCs) is proposed, considering the uncertainty of current loading. First, the structure and operating modes of FIC are analyzed. Based on the fault tree analysis, the reliability model of single-terminal MMC is established. Next, considering the impact of random current loading on the IGBT modules’ reliability, Monte Carlo simulation is used to obtain the loading expectation correction factor, thus the equivalent reliability model of IGBT module is built. Furthermore, the state space model of FIC is established, and the analytical method based on Markov chain is used to solve it. Taking the improved three IEEE33 node feeder groups as the testing system, the equivalent reliability indices of IGBT module as well as the converter reliability of the three terminals of MMC are obtained via simulation, and based on which, the probabilities and average durations of FIC’s eight states are calculated to verify the proposed model.