This paper presents a control scheme based on the predictive control theory and Petri nets (PNs) formalism to control a flying capacitor multilevel converter. The proposed scheme takes advantage of the benefits offered by the finite control set-model predictive control (FCS-MPC) methodology and the versatility of PNs to regulate the capacitor voltages and output current, simultaneously. The inclusion of PNs allows us to simplify the control scheme. A first PN is used to select, from a subset of switching states, the switching state that accomplishes both control objectives. This approach reduces the computational burden if compared with a typical predictive control scheme. Furthermore, a PN-based prediction scheme is used to predict the capacitor voltages. This prediction scheme uses only measurements of output voltage and current, which reduces the number of required sensors. This approach allows us to implement the internal capacitor voltages control independently if a multileg configuration is needed. The scheme is experimentally validated in a five-level flying capacitor multilevel converter.