In this paper the adaptive control of the DC/DC boost converter supplied by the fuel cell is described. The mathematical models of PEM fuel cell and DC/DC boost converter controlled in voltage and current mode, as well as in continuous and discontinuous conduction modes are given. The linear mathematical models of the boost converter and boost converter supplied by the emulator of the fuel cell BCS 64-32 are determined experimentally. A basic PI controller is designed for operating point determined by boost converter’s nominal power. Deviations from the nominal operating point are compensated by the adaptive controller with reduced order reference model and signal adaptation with a reduced vector of state variables. Using the reduced order algorithm, the number of error weighting coefficients in the algorithm is reduced. The procedure for determining the adaptive algorithm’s weighting coefficients, based on a combination of poles and zeros placement method and optimization method is proposed. After applying the proposed requirements based on the method of poles and zeros placement, the optimal adaptive algorithm’s weighting coefficients can be determined in just a few iterations, without use of computer, thus greatly facilitating the application of the algorithm on real systems. Simulation and experimental results show that the dynamic behavior of highly nonlinear control system with the fuel cell and DC/DC boost converter, either in continuous, or in discontinuous conduction mode, can be fairly accurately described the dynamic behavior of the reference model, i.e., the linear system with fixed parameters.