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 J124353.93 +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 +/- 0.08 mag and the bolometric luminosity is L-bol = (1.4 +/- 0.1) x 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 C IV line is blueshifted and there is indication of broad absorption lines. The Mg IT-based black hole mass is M-BH = (3.3 +/- 2.0) x 10(8) M-circle dot, thus indicating a moderate mass accretion rate with an Eddington ratio) lambda(Edd) = 0.34 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.