We have successfully synthesized the high-quality single crystals of double perovskite La2CoMnO6 by flux method and investigated the effects of different annealing conditions on the magnetic properties. In an as-grown crystal, ferromagnetic order along the c axis arises below 204 K, and the spin-glass-type behavior inherent from ionic disorders is also observed. Upon annealing in different gas environments, the reconstructed magnetic states induce a metamagnetic transition (after Ar annealing), and increase Curie temperature (after O2 annealing). After quenching, the magnetic transition temperature decreases significantly, comprising lots of defects and disorders. Our results provide adequate procedures to control magnetic properties of double-perovskite compounds.