The Born cross sections of the e+e−→Σ+Σ¯− and e+e−→Σ−Σ¯+ processes are determined for center-of-mass energy from 2.3864 to 3.0200 GeV with the BESIII detector. The cross section lineshapes can be described properly by a pQCD function and the resulting ratio of effective form factors for the Σ+ and Σ− is consistent with 3. In addition, ratios of the Σ+ electric and magnetic form factors, |GE/GM|, are obtained at three center-of-mass energies through an analysis of the angular distributions. These measurements, which are studied for the first time in the off-resonance region, provide precision experimental input for understanding baryonic structure. The observed new features of the Σ± form factors require more theoretical discussions for the hyperons. © 2021 The Author(s)