The invention relates to a reconfigurable beam reflectarray antenna for frequencies in the terahertz and millimeter-wave range. The reflectarray antenna consists of a flat array of phase-shifter cells (reflectarray) illuminated by a feeder, which produces an electronically reconfigurable collimated or shaped beam, in which the phase-shifter cells are formed by multiple stacked layers of conductive elements on a dielectric substrate, alternated with layers of liquid crystal and a conductive plane. By applying bias voltages to the conductive elements, the dielectric constant of the liquid crystal is varied, thereby producing a phase shift in the reflected field in each phase shifter cell and allowing electronic beam scanning or reconfiguration to be performed. The bandwidth and the performance of the beam scanning or reconfiguration are improved by including multiple layers of conductive elements and liquid crystal. The antenna is suitable for observation satellites, communications and security systems.