We report the discovery of a quasar at z = 7.07 , which was selected from the deep multi-band imaging data collected by the Hyper Suprime-Cam ( HSC ) Subaru Strategic Program survey . This quasar , HSC J 124353.93 + 010038.5 , has an order of magnitude lower luminosity than do the other known quasars at z > 7 . The rest-frame ultraviolet absolute magnitude is M _ { 1450 } = -24.13 \pm 0.08 mag and the bolometric luminosity is L _ { bol } = ( 1.4 \pm 0.1 ) \times 10 ^ { 46 } erg s ^ { -1 } . Its spectrum in the optical to near-infrared shows strong emission lines , and shows evidence for a fast gas outflow , as the \ion C4 line is blueshifted and there is indication of broad absorption lines . The \ion Mg2-based black hole mass is M _ { BH } = ( 3.3 \pm 2.0 ) \times 10 ^ { 8 } M _ { \odot } , thus indicating a moderate mass accretion rate with an Eddington ratio \lambda _ { Edd } = 0.34 \pm 0.20 . It is the first z > 7 quasar with sub-Eddington accretion , besides being the third most distant quasar , known to date . The luminosity and black hole mass are comparable to , or even lower than , those measured for the majority of low- z quasars discovered by the Sloan Digital Sky Survey , and thus this quasar likely represents a z > 7 counterpart to quasars commonly observed in the low- z universe .