To reduce image artifacts of proton computed tomography (pCT) from a preclinical scanner, for imaging of the relative stopping power (RSP) needed for particle therapy treatment planning using a simple empirical artifact correction method. We adapted and employed a correction method previously used for beam-hardening correction in x-ray CT which makes use of a single scan of a custom-built homogeneous phantom with known RSP. Exploiting the linearity of the filtered backprojection operation, a function was found which corrects water-equivalent path lengths (RSP line integrals) in experimental scans using a prototype pCT scanner. The correction function was applied to projection values of subsequent scans of a homogeneous water phantom, a sensitometric phantom with various inserts and an anthropomorphic head phantom. Data were acquired at two different incident proton energies to test the robustness of the method. Inaccuracies in the detection process caused an offset and known ring artifacts in the water phantom which were considerably reduced using the proposed method. The mean absolute percentage error (MAPE) of mean RSP values of all inserts of the sensitometric phantom and the water phantom was reduced from 0.87% to 0.44% and from 0.86% to 0.48% for the two incident energies respectively. In the head phantom a clear reduction of artifacts was observed. Image artifacts of experimental pCT scans with a prototype scanner could substantially be reduced both in homogeneous, heterogeneous and anthropomorphic phantoms. RSP accuracy was also improved.