Abstract A new, fast and flexible, time-dependent, one-dimensional numerical model was developed in order to study in detail the operation of an active magnetic regenerator (AMR). The model is based on a coupled system of equations (for the magnetocaloric material and the heat-transfer fluid) that have been solved simultaneously with the software package MATLAB. The model can be employed to analyze a wide range of different operating conditions (mass-flow rate, operating frequency, magnetic field change), different AMR geometries, different magnetocaloric materials and heat-transfer fluids, layered and single-bed AMRs, etc. This paper also presents an optimization of the AMR’s geometry, where the AMR consists of a packed-bed of grains (spheres) of gadolinium (Gd). The optimization of the mass-flow rate and the operating frequency of the AMR were performed by studying five different diameters of Gd spheres.