We have initiated a new survey for local extremely metal-poor galaxies ( EMPGs ) with Subaru/Hyper Suprime-Cam ( HSC ) large-area ( \sim 500 deg ^ { 2 } ) optical images reaching a 5 \sigma limit of \sim 26 magnitude , about 100 times deeper than the one of Sloan Digital Sky Survey ( SDSS ) . To select Z / Z _ { \odot } < 0.1 EMPGs from \sim 40 million sources detected in the Subaru images , we first develop a machine-learning ( ML ) classifier based on a deep neural network algorithm with a training data set consisting of optical photometry of galaxy , star , and QSO models . We test our ML classifier with SDSS objects having spectroscopic metallicity measurements , and confirm that our ML classifier accomplishes 86 % -completeness and 46 % -purity EMPG classifications with photometric data . Applying our ML classifier to the photometric data of the Subaru sources as well as faint SDSS objects with no spectroscopic data , we obtain 27 and 86 EMPG candidates from the Subaru and SDSS photometric data , respectively . We conduct optical follow-up spectroscopy for 10 out of our EMPG candidates with Magellan/LDSS-3 + MagE , Keck/DEIMOS , and Subaru/FOCAS , and find that the 10 EMPG candidates are star-forming galaxies at z = 0.007 - 0.03 with large H \beta equivalent widths of 104–265 Å , stellar masses of \log ( M _ { \star } /M _ { \odot } ) = 5.0–7.1 , and high specific star-formation rates of \sim 300 Gyr ^ { -1 } , which are similar to those of early galaxies at z \gtrsim 6 reported recently . Our metal-poor galaxies have small velocity dispersions of nebular gas ( 27.8–32.5 km s ^ { -1 } ) and are significantly located in the relatively isolated environment compared to typical , local galaxies . We spectroscopically confirm that 3 out of 10 candidates are truly EMPGs with Z / Z _ { \odot } < 0.1 , one of which is HSC J1631 + 4426 , the most metal-poor galaxy with Z / Z _ { \odot } = 0.021 so far identified among star-forming galaxies in the low-mass regime of \log ( M _ { \star } /M _ { \odot } ) < 6.0 .