The magnetocaloric effect (MCE) is described by the change in temperature of a material by magnetic field variation and is a crucial subject in magnetism; it is motivated by the desire to enhance energy-efficient magnetic refrigeration for clean technology. Despite the recent discovery of the giant cryogenic MCE in double perovskites, the role of magnetic anisotropy has not yet been clearly discussed, because of the averaging effect of polycrystalline samples. Here, we investigated the anisotropic MCE in the single-crystal double perovskite Gd2CoMnO6. In addition to the ferromagnetic order of the Co2+ and Mn4+ moments, the large Gd3+ moments align below T Gd = 21 K, exhibiting an isotropic nature. Because of the intricate temperature development of magnetically hysteretic behaviour and metamagnetism, the change in magnetic entropy along the c-axis appears to be relatively small. On the contrary, the smaller but almost reversible magnetization perpendicular to the c-axis leads to a large MCE with a maximum entropy change of 25.4 J/kg·K. The anisotropic MCE generates a giant rotational MCE, estimated as 16.6 J/kg·K. Our results demonstrate the importance of magnetic anisotropy for understanding the MCE and reveal essential clues for exploring suitable magnetic refrigerant compounds aiming at magnetic functional applications.