Recently, we measured the 70Zn(n,γ)71Znm activation cross sections using the 7Li(p,n)7Be neutron source for 2.0 MeV < Ep < 3.7 MeV. Since the time-of-flight and multiple foil activation techniques cannot be applied due to the continuous beam structure and weak neutron flux at the facility, we have to rely on calculated neutron energy spectra for data reduction procedure. There are existing Monte Carlo–based codes such as Protons In Neutrons Out (PINO) and SimLiT for calculation of 7Li(p,n)7Be neutron source spectra at these energies. However, these two codes predicted different neutron spectra at these energy regions. We therefore decided to study the thick and thin target 7Li(p,n)7Be neutron spectra from the reaction threshold to the three-body breakup threshold by deterministic calculation. The predicted neutron spectra near threshold were validated by experimental neutron spectra. Our neutron spectra were compared with those predicted by PINO and SimLiT. Our neutron spectra at Ep = 2.8 and 3.5 MeV agree perfectly with those predicted by SimLiT but not with those predicted by PINO.