9Be(p,xn) and 7Li(p,xn) are two reactions for the accelerator-based compact neutron source at low energy protons conditions, especially for BNCT facilities and it is necessary to simulate the beam characteristics accurately. The different reference physics lists recommended by GEANT4 have been used to calculate the neutron beam characteristics for the 9Be and 7Li targets bombarded by proton beams of 5 ∼ 10 MeV and the accuracy of GEANT4 simulations has been discussed. By comparing with the reference data such as experimental data, MCNP6 simulations and numerical calculations, the results calculated by QGSP_BIC_AllHP show good agreement with a relative error of less than 10%. The neutron yields level out and have a tendency to move forward, when the thickness is greater than the range of protons in targets. However, the neutron yields are significantly underestimated by other physics lists except for QGSP_BIC_AllHP. In addition, two fitted curve equations are acquired to quickly estimate the neutron yield for 9Be and 7Li targets below 20 MeV. Therefore, due to the limitation of the particle type and energy range in this study, GEANT4 with QGSP_BIC_AllHP is recommended to calculate hadronic interactions of protons with matter below 20 MeV.