The yields of KS0 mesons have been measured in inelastic p+p interactions at incident projectile momenta of 31, 40 and 80 GeV/c (sNN=7.7,8.8 and 12.3 GeV, respectively). The data were recorded by the NA61/SHINE spectrometer at the CERN Super Proton Synchrotron and the KS0 mesons identified via their decays into π+π- pairs. Double-differential distributions are presented as function of transverse momentum and rapidity. The mean multiplicities of KS0 mesons were determined to be (5.95±0.19(stat)±0.30(sys))×10-2 at 31 GeV/c, (7.61±0.13(stat)±0.43(sys))×10-2 at 40 GeV/c and (11.58±0.12(stat)±0.55(sys))×10-2 at 80 GeV/c. The results on KS0 production are compared with the production of charged kaons in corresponding reactions and with model calculations (Epos1.99, SMASH 2.0 and PHSD) as well as with published data from other experiments.