Magnetic properties can be manipulated to enhance certain functionalities by tuning different material processing parameters. Here, we present the controllable magnetization steps of hysteresis loops in double-perovskite single crystals of Eu2CoMnO6. Ferromagnetic order emerges below T-C approximate to 122 K along the crystallographic c axis. The difficulty in altering Co2+ and Mn4+ ions naturally induces additional antiferromagnetic clusters in this system. Annealing the crystals in different gas environments modifies the mixed magnetic state, and results in the retardation (after O-2-annealing) and bifurcation (after Ar-annealing) of the magnetization steps of isothermal magnetization. This remarkable variation offers an efficient approach for improving the magnetic properties of double-perovskite oxides.