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 O-2 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. (C) 2015 Elsevier B.V. All rights reserved.