A neutron spectrometer, the European Low-Energy Neutron Spectrometer (ELENS), has been constructed to study exotic nuclei in inverse-kinematics experiments. The spectrometer, which consists of plastic scintillator bars, can be operated in the neutron energy range of 100 keV to 10 MeV. The neutron energy is determined using the time-of-flight technique, while the position of the neutron detection is deduced from the time-difference information from photomultipliers attached to both ends of each bar. A novel wrapping method has been developed for the plastic scintillators. The array has a larger than 25% detection efficiency for neutrons of approximately 500 keV in kinetic energy and an angular resolution of less than 1 degree. Details of the design, construction and experimental tests of the spectrometer will be presented.