This work presents measurements done at the Peking University Van de Graaff neutron source of the response of single crystal synthetic diamond (SD) detectors to quasi-monoenergetic neutrons of 14-20 MeV. The results show an energy resolution of 1% for incoming 20 MeV neutrons, which, together with 1% detection efficiency, opens up to new prospects for fast ion physics studies in high performance nuclear fusion devices such as SD neutron spectrometry of deuterium-tritium plasmas heated by neutral beam injection.