The study of two-dimensional (2D) magnetic materials has driven the development of modern nano-electronic devices. Exploration of novel intrinsic layered materials with 2D magnetic order will provide a material candidate pool for fabricating 2D devices and searching for new quantum phases. Recently the layered antiferromagnetic (AF) topological insulators have aroused the great interest of researchers. As one of the proposed axion insulators, EuIn₂As₂ exhibits a layered structure and 2D AF order. It is found that the parent compound EuIn₂As₂ exhibits metallic behavior instead of the predicted insulating feature. To pursuit the predicted non-trivial topological state and novel feature, in this paper, we use various elements to dope the system to adjust the Fermi level. It is found that only Ca is successfully doped into the EuIn₂As₂ system. The systematic transport and magnetization studies are performed on the single crystal of Eu_1–xCa_xIn₂As₂. The long-range AF order is revealed to be similar to the parent compound. Above the AF transition, the magnetization violated Curie-Weiss behavior and magnetoresistance keeps negative, indicating the ferromagnetic order. With doping nearly 20% non-magnetic Ca, the magnetic properties of the system barely change, which is favorable to keeping the former predicted nontrivial topological properties in EuIn₂As₂. Although Ca shares the same valence with Eu, the carrier density of Eu_1–xCa_xIn₂As₂ is one order lower than that of EuIn₂As₂. The Ca doping brings electrons in and lifts the Fermi level. The results enrich the 2D magnetic material candidate pool and provide useful information for realizing the nontrivial topological state in the 2D AF system.