This article presents a systematic analysis and design of the X-band Minkowski reflectarray antenna (RA) by using the 3-D Computer Simulation Technology Microwave Studio (CST MWS)-based multilayer perceptron neural network (MLP NN) model of a unit element. This MLP NN model is utilized efficiently as a fast and accurate model within a particle swarm optimization procedure to determine the calibration phasing characteristic belonging to the resultant optimum patch geometry and substrate. In design stage, the MLP NN analysis model is reversed to determine the variable-size of each reflectarray element to meet the necessary phase delay with the adaptive iterative step. In the final stage, the optimum Minkowski RA consisting of the variable-size Minkowski patches interspaced by 0.5 wavelength at the frequency of 11 GHz on the Taconic RF-35 with epsilon(r) = 3.54, tan delta = 0.0018 and the optimum thickness (h(opt)) are analyzed using the 3D CST MWS and compared with the counterpart square and parabolic reflectors. Compared with the counterpart RA with square element and the parabolic reflector, this optimized Minkowski RA is resulted to be capable of providing higher realized gain and lower sidelobe level (SLL). Furthermore, the effect of feed movement along the focal length on the gain-bandwidth and radiation pattern is also worked out and demonstrated. It is concluded that this method can also be applied as a robust method for the design and analysis of a RA built by arbitrarily shaped patches. (C) 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 23: 272-284, 2013.