The energy resolution of a neutron time-of-flight spectrometer designed for diagnosing deuterium fusion plasmas has been studied and optimized using numerical methods. The spectrometer consists of two spatially separated sets of fast plastic scintillators. The first set is exposed to a collimated neutron flux from the fusion plasma. The second set, which is located outside the direct neutron flux, is used to detect elastically n(p,p')n' scattered neutrons from the first set. From the measured neutron time-of-flight, the energy spectrum of the observed neutrons is deduced. A code has been developed to simulate the neutron scattering process in the spectrometer components and to calculate the energy resolution as a function of detector geometry parameters. It is shown that it is possible to extend the size of the detectors in order to improve the detection efficiency, with a minimum degradation of the energy resolution, provided the detectors are arranged in an optimal way. The knowledge thus gained has been used at the Joint European Torus (JET) tokamak. The calculated energy resolution of the time-of-flight neutron spectrometer, which was in use at JET until1990 and has now been upgraded, is presented. The technique is not limited toD-D neutrons, but is applicable to any neutron source of sufficient strength in the MeV-range.