This paper describes the design of multi-beam reflector antennas that were installed on the satellite mission as part of a microwave radiometer (MWR, Microwave Water Radiometer) in the K and Ka bands. The objective of the mission was to detect geophysical parameters for the analysis of global water cycle, factor of importance to study climate change. An optimal result was obtained with a toroidal offset parabolic reflector that allows its use with multiple beams. Due to satellite mission requirements Earth was observed laterally to its trajectory, causing an asymmetrical arrangement of the antenna´s beam design. In this paper the design of the reflector to achieve eight asymmetric beam location is analyzed, using simulation and applying Geometrical Optics analytical methods, to evaluate its characteristics.