A fast neutron spectrometer consisting of segmented plastic scintillator and 3Heproportional counters was constructed for the measurement of neutrons in the energy range 1–200MeV. We discuss its design, principles of operation, and the method of analysis. The detector is capable of observing very low neutron fluxes in the presence of ambient gamma background and does not require scintillator pulse-shape discrimination. The spectrometer was characterized for its energy response in fast neutron fields of 2.5MeV and 14MeV, and the results are compared with Monte Carlo simulations. Measurements of the fast neutron flux and energy response at 120m above sea-level (39.130°N, 77.218°W) and at a depth of 560m in a limestone mine are presented. Finally, the design of a spectrometer with improved sensitivity and energy resolution is discussed.