We report on the detection and subsequent X-ray monitoring of the new Galactic black hole candidate MAXI J1535-571 with the MAXI/GSC. Afterthe discovery on 2017 September 2 made independently with MAXI and the Swift/BAT, the source brightened gradually, and in a few weeks, reached the peak intensity of ~5 Crab, or ~1.6 x 10^{-7} erg cm^{-2} s^{-1} in terms of the 2--20 keV flux. On the initial outburst rise, the X-ray spectrum was described by a power-law model with a photon index of ~2, while after a hard-to-soft transition which occurred on September 18, the spectrum required a disk blackbody component in addition. At around the flux peak, the 2-8 keV and 15-50 keV light curves showed quasi-periodic and anti-correlated fluctuations with an amplitude of 10--20%, on a time scale of ~1-day. Based on these X-ray properties obtained with the MAXI/GSC, we discuss the evolution of the spectral state of this source, and give constraints on its system parameters.