This paper presents an alternative approach to the flow control of an oxidizer in a proton exchange membrane (PEM) fuel cell system in which pure oxygen is the gas supplied to the cathode channel of the stack. The proposed oxygen flow control is implemented based on information about the current drawn from the fuel cell stack and the voltage variation in the stack. This information and a fuzzy-logic-based control algorithm are used to increase oxygen utilization in a PEM fuel cell system without a recirculation system in relation to the control, in which the oxygen flow rate is determined only in proportion to the current drawn from the stack. To verify the validity of the adopted assumptions, simulation tests of the proposed fuzzy control algorithm were conducted, for which parameters were adopted arbitrarily and determined with help of genetic algorithms. For simulation research, the proposed empirical mathematical model was used, which describes the mathematical relationship between voltage variation in the stack and the stoichiometry of oxygen flow through the cathode of a fuel cell stack. The simulation results confirm that the proposed control method leads to an increase in the oxygen utilization in the system without oxygen recirculation compared to an open system with cathode stoichiometry set to a constant level.