We report here our latest search for molecular outflows from young brown dwarfs and very low-mass stars in nearby star-forming regions. We have observed three sources in Taurus with the Submillimeter Array and the Combined Array for Research in Millimeter-wave Astronomy at 230 GHz frequency to search for CO J=2-1 outflows. We obtain a tentative detection of a redshifted and extended gas lobe at about 10 arcsec from the source GM Tau, a young brown dwarf in Taurus with an estimated mass of 73 M_J, which is right below the hydrogen-burning limit. No blueshifted emission around the brown dwarf position is detected. The redshifted gas lobe that is elongated in the northeast direction suggests a possible bipolar outflow from the source with a position angle of about 36 degrees. Assuming that the redshifted emission is outflow emission from GM Tau, we then estimate a molecular outflow mass in the range from 1.9x10^-6 M_Sun to 2.9x10^-5 M_Sun and an outflow mass-loss rate from 2.7x10^-9 M_Sun yr^-1 to 4.1x10^-8 M_Sun yr^-1. These values are comparable to those we have observed in the young brown dwarf ISO-Oph 102 of 60 M_J in rho Ophiuchi and the very low-mass star MHO 5 of 90 M_J in Taurus. Our results suggest that the outflow process in very low-mass objects is episodic with duration of a few thousand years and the outflow rate of active episodes does not significantly change for different stages of the formation process of very low-mass objects. This may provide us with important implications that clarify the formation process of brown dwarfs.