We present the first results on the new black hole candidate, MAXI J1305-704, observed by MAXI/GSC. The new X-ray transient, named as MAXI J1305-704, was first detected by the MAXI-GSC all-sky survey on 2012 April 9 in the direction to the outer Galactic bulge at (l,b)=(304.2deg,-7.6deg). The Swift/XRT follow-up observation confirmed the uncatalogued point source and localized to the position at (13h06m56s.44,-70d274.91). The source continued the activity for about five months until 2012 August. The MAXI/GSC light curve in the 2--10 keV band and the variation of the hardness ratio of the 4-10 keV to the 2-4 keV flux revealed the hard-to-soft state transition on the the sixth day (April 15) in the brightening phase and the soft-to-hard transition on the ~60th day (June 15) in the decay phase. The luminosity at the initial hard-to-soft transition was significantly higher than that at the soft-to-hard transition in the decay phase. The X-ray spectra in the hard state are represented by a single power-law model with a photon index of ~2.0, while those in the soft state need such an additional soft component as represented by a multi-color disk blackbody emission with an inner disk temperature ~0.5--1.2 keV. All the obtained features support the source identification of a Galactic black-hole binary located in the Galactic bulge.