We construct a new global optical model potential to describe the elastic scattering of 12C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.