To validate the accuracy of the general-purpose Monte Carlo Particle and Heavy-Ion Transport code System (PHITS), a benchmark study of the recent version (version 3.24) of PHITS has been conducted using neutron-shielding experiments listed in the Shielding Integral Benchmark Archive and Database (SINBAD). Five neutron sources were selected, which are generated from (1) 43- and 68-MeV proton-induced reaction on a thin lithium target, (2) 52-MeV proton-induced reaction on a thick graphite target, (3) 590-MeV proton-induced reaction on a thick lead target, (4) 500-MeV proton-induced reaction on a thick tungsten target, and (5) 800-MeV proton-induced reaction on a thick tantalum target. For all these cases, overall agreements between the experimental and calculated results were satisfactory to simulate neutron- and proton-induced reactions up to 200 MeV when using the Japanese evaluated nuclear data library JENDL-4.0/HE; however, using default settings in the code system made discrepancies between the results in neutron production and scatterings in shielding materials with energies lower than 100 MeV. The present study revealed that it is preferable to use JENDL-4.0/HE in the PHITS calculation.