The Born cross sections of e+e−→Σ0Σ¯0 are measured at center-of-mass energies from 2.3864 to 3.0200 GeV using data samples with an integrated luminosity of 328.5 pb−1 collected with the BESIII detector operating at the BEPCII collider. The analysis makes use of a novel reconstruction method for energies near production threshold, while a single-tag method is employed at other center-of-mass energies. The measured cross sections are consistent with earlier results from BaBar, with a substantially improved precision. The cross-section lineshape can be well described by a perturbative QCD-driven energy function. In addition, the effective form factors of the Σ0 baryon are determined. The results provide precise experimental input for testing various theoretical predictions.