In inertial confinement fusion experiments that involve short-laser pulses such as fast ignition (FI), diagnosis of neutrons is usually very challenging because high-intensity γ rays generated by short-laser pulses would mask the much weaker neutron signal. In this paper, fast-response scintillators with low afterglow and gated microchannel plate photomultiplier tubes are combined to build neutron time-of-flight (nTOF) spectrometers for such experiments. Direct-drive implosion experiments of deuterium-gas-filled capsules were performed at the Shenguang-II Upgrade (SG-II-UP) laser facility to study the compressed fuel areal density (〈ρR〉) and evaluate the performance of such nTOF diagnostics. Two newly developed quenched liquid scintillator detectors and a gated ultrafast plastic scintillator detector were used to measure the secondary DT neutrons and primary DD neutrons, respectively. The secondary neutron signals were clearly discriminated from the γ rays from (n, γ) reactions, and the compressed fuel areal density obtained with the yield-ratio method agrees well with the simulations. Additionally, a small scintillator decay tail and a clear DD neutron signal were observed in an integrated FI experiment as a result of the low afterglow of the oxygen-quenched liquid scintillator.