Massive molecular outflows erupting from high-mass young stellar objects provide important clues to understanding the mechanism of high-mass star formation. Based on new CO J=3-2 and J=1-0 observations using the Atacama Submillimeter Telescope Experiment (ASTE) and Mopra telescope facilities, we discovered a massive bipolar outflow associated with the dense dust core AGALG337.916-00.477 (AGAL337.9-S), located 3.48 kpc from the Sun. The outflow lobes have extensions of less than 1 pc -and thus were not fully resolved in the angular resolutions of ASTE and Mopra- and masses of 35-40 M_sun. The maximum velocities of the outflow lobes are as high as 35-40 km/s. Our analysis of the infrared and sub-mm data indicates that AGAL337.9-S is in an early evolutionary stage of the high-mass star formation, having the total far-infrared luminosity of ~5x10^4 L_sun. We also found that another dust core AGALG337.922-00.456 (AGAL337.9-N) located 2 north of AGAL337.9-S is a high-mass young stellar object in an earlier evolutional stage than AGAL337.9-S, although it is less bright in the mid-infrared than AGAL337.9-S.