A position-sensitive detector has been developed for studying small angle scattering of fast neutrons. The detector mainly consists of two photomultiplier tubes to monitor the liquid scintillator. The time difference between two signals from two photomultiplier tubes is used to determine the position of light emitted. The 14.7 MeV neutron elastic scattering differential cross section of Zr, Nb, Ti and Pb were measured by position-sensitive detector and associated particle time-of-flight method at the angles from 3 deg to 15 deg. The corrections for neutron fluence attenuation, multiple scattering and finite geometry are performed by using Monte-Carlo method. The experimental results provide data needed in nuclear engineering design.