Multilevel converters are mainly used in the medium-voltage high-power applications. Flying capacitor multicell (FCM) converter is one of the well-known categories of multilevel power converters. Since conduction power loss investigation can be very advantageous in the design step of multilevel converters, this paper presents an analytic approach in order to calculate and investigate the conduction power loss in FCM converters. First, the rms and average currents of the insulated gate bipolar transistors (IGBTs) and anti-parallel diodes are analytically calculated by considering the associated duty cycle of each IGBT and anti-parallel diode, power converter modulation index, load current, and load power factor. Numerical results of the obtained analytical equations to calculate the rms and average currents of the IGBTs/diodes are compared against the simulation results whereas matching well and confirming accuracy of the derived formula. Afterwards, the obtained equations for the rms and average currents computation are used to calculate conduction power losses in a 12.25MVA 3.3kV 9-level (line-to-line) FCM power converter. A 2.5kV 1.5kA IGBT module from ABB is considered as power switches for FCM converter in performed case study.