An irreversible magnetic Brayton refrigeration-cycle model is established, in which the thermal resistance and irreversibility in the two adiabatic processes are taken into account. Based on the model, the performance characteristics of the magnetic Brayton refrigeration-cycle are investigated and the effects of the irreversibilities and the ratio of the magnetic fields in the two iso-field processes on the performance of the refrigeration cycle are revealed. On the basis of the thermodynamic properties of a paramagnetic material, by using the optimal control-theory, the mathematical expressions for the cooling load and the coefficient of performance are derived and some important performance parameters, e.g., the temperatures of the working substance at several important state-points, are optimized. By means of numerical predictions, the optimal performance characteristic curves of the magnetic Brayton refrigeration-cycle are obtained and analyzed. Furthermore, some optimal operating-regions including those for the cooling load, coefficient of performance and the temperatures of the cyclic working substance at the two important state-points are determined and evaluated. Finally, several special cases are discussed in detail. (c) 2007 Elsevier Ltd. All rights reserved.