We performed a novel Σ+p scattering experiment at the J-PARC Hadron Experimental Facility. Approximately 2400 Σ+p elastic scattering events were identified from 4.9 × 107 tagged Σ+ particles in the Σ+ momentum range 0.44–0.80 GeV/c. The differential cross sections of the Σ+p elastic scattering were derived with much better precision than in previous experiments. The obtained differential cross sections were approximately 2 mb/sr or less, which were not as large as those predicted by the fss2 and FSS models based on the quark cluster model in the short-range region. By performing phase-shift analyses for the obtained differential cross sections, we experimentally derived the phase shifts of the 3S1 and 1P1 channels for the first time. The phase shift of the 3S1 channel, where a large repulsive core was predicted owing to the Pauli effect between quarks, was evaluated as $20^\circ \lt |\delta _{^3S_1}|\lt 35^\circ$. If the sign of $\delta _{^3S_1}$ is assumed to be negative, the interaction in this channel is moderately repulsive, as the Nijmegen extended-sort-core models predicted.