Dirac electrons are known to exhibit anomalous orbital diamagnetism arising from their linear energy dispersion, which is one of their characteristic properties. In real Dirac electrons systems, however, a background magnetization from conventional electrons makes it difficult to isolate the contribution from Dirac electrons experimentally. Here, we focus on an organic conductor hosting a two-dimensional Dirac electron system, which provides an ideal platform with a simple Dirac band structure and the Fermi energy located at the Dirac point. We focus on the characteristic magnetic-field dependence of the magnetization of Dirac-electron and successfully separate it from the conventional diamagnetic background through magnetic torque measurements using a highly sensitive microcantilever.