Recently, the increasing research on the anisotropic optical axis (OA) has provided a novel way to control light. However, this method is rarely applied to modulate the near-field radiative heat transfer (NFRHT). In this work, we investigate the influences of the OA orientation of calcite on the NFRHT between two calcite parallel structures. The numerical results demonstrate that the near-field radiative heat flux is larger when the OA is along the z-axis than that when the OA is along the x-axis. This is because when the OA is along the z-axis, the excited hyperbolic polaritons exhibit a full range of angles in the type I hyperbolic band. In contrast, the excited hyperbolic polaritons exhibit a finite angle when the OA is along the x-axis. Moreover, it is further investigated that the thickness has a significant impact on the NFRHT between calcite slabs. Our findings may highlight the promising role of calcite in manipulating NFRHT.