Brown dwarfs are important objects because they may provide a missing link between stars and planets, two populations that have dramatically different formation histories. In this paper, we present the candidate binaries with brown dwarf companions that are found by analyzing binary microlensing events discovered during the 2004-2011 observation seasons. Based on the low mass ratio criterion of q <0.2, we found seven candidate events: OGLE-2004-BLG-035, OGLE-2004-BLG-039, OGLE-2007-BLG-006, OGLE-2007-BLG-399/MOA-2007-BLG-334, MOA-2011-BLG-104/OGLE-2011-BLG-0172, MOA-2011-BLG-149, and MOA-201-BLG-278/OGLE-2011-BLG-012N. Among them, we are able to confirm that the companions of the lenses of MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149 are brown dwarfs by determining the mass of the lens based on the simultaneous measurement of the Einstein radius and the lens parallax. The measured masses of the brown dwarf companions are 0.02 ± 0.01 M⊙ and 0.019 ± 0.002 M⊙ for MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149, respectively, and both companions are orbiting low-mass M dwarf host stars. More microlensing brown dwarfs are expected to be detected as the number of lensing events with well-covered light curves increases with new-generation searches.