The fission reactions of 238U induced by D-T neutrons were investigated by neutron activation technique and low-background HPGe-γ spectrometer. The half-life was used to identify the possible daughter nuclide. The fission cross-sections of 238U(n,f)89Rb reaction induced at the neutron energy around 14 MeV, i.e., 14.1 ± 0.3, 14.5 ± 0.3 and 14.7 ± 0.3 MeV, were measured precisely. The neutron flux was monitored by accompanying α-particle of the T(d,n)4He reaction and the neutron energies were determined by the cross-section ratio of 90Zr(n,2n)89Zr to 93Nb(n,2n)92mNb reaction. The fission cross-sections of the 238U(n,f)89Rb reaction are 33.2 ± 2.1 mb, 32.2 ± 2.0 mb, and 32.6 ± 2.1 mb, corresponding to the above neutron energy points.