Imaging of positrons induced by nuclear reactions with a proton beam is a possible method for observing the beam shape from outside the subject. However, such imaging of induced positrons has so far been conducted for solid materials. The induced positron distribution in liquid water has not been measured or reported. To clarify the distribution of induced positrons in liquid water, we conducted Cherenkov-light imaging after irradiation by protons to a water phantom. After irradiation by a 117-MeV proton beam to a phantom containing liquid water, Cherenkov-light imaging of the induced positrons was conducted using a cooled charge-coupled device (CCD) camera following the decay of the positrons. We also imaged the luminescence of water during irradiation by the proton beam to compare the distributions. We could measure the distribution of Cherenkov-light from the induced positrons in liquid water. Positron distributions kept their beam shapes in water but were different from that of the luminescence image; positron distribution was wider in the deep area of the beams in the lateral as well as depth direction. The distributions' shapes were only slightly changed with time. We conclude that Cherenkov-light imaging from the induced positrons after irradiation by a proton beam in water was possible, and we found that the induced positrons kept their beam shape in water with different shape from that of dose. These findings may provide new insights for imaging in particle therapy.