Using data samples collected with the BESIII detector at the BEPCII collider, we measure the Born cross section of e+e−→pp¯ at 12 center-of-mass energies from 2232.4 to 3671.0 MeV. The corresponding effective electromagnetic form factor of the proton is deduced under the assumption that the electric and magnetic form factors are equal (|GE|=|GM|). In addition, the ratio of electric to magnetic form factors, |GE/GM|, and |GM| are extracted by fitting the polar angle distribution of the proton for the data samples with larger statistics, namely at s√=2232.4 and 2400.0 MeV and a combined sample at s√=3050.0, 3060.0 and 3080.0 MeV, respectively. The measured cross sections are in agreement with recent results from BABAR, improving the overall uncertainty by about 30%. The |GE/GM| ratios are close to unity and consistent with BABAR results in the same q2 region, which indicates the data are consistent with the assumption that |GE|=|GM| within uncertainties.