We present the results from a search for new Milky Way ( MW ) satellites from the first two years of data from the Hyper Suprime-Cam ( HSC ) Subaru Strategic Program ( SSP ) \sim 300 deg ^ { 2 } and report the discovery of a highly compelling ultra-faint dwarf galaxy candidate in Cetus . This is the second ultra-faint dwarf we have discovered after Virgo I reported in our previous paper . This satellite , Cetus III , has been identified as a statistically significant ( 10.7 \sigma ) spatial overdensity of star-like objects , which are selected from a relevant isochrone filter designed for a metal-poor and old stellar population . This stellar system is located at a heliocentric distance of 251 ^ { +24 } _ { -11 } kpc with a most likely absolute magnitude of M _ { V } = -2.4 \pm 0.6 mag estimated from a Monte Carlo analysis . Cetus III is extended with a half-light radius of r _ { h } = 90 ^ { +42 } _ { -17 } pc , suggesting that this is a faint dwarf satellite in the MW located beyond the detection limit of the Sloan Digital Sky Survey . Further spectroscopic studies are needed to assess the nature of this stellar system . We also revisit and update the parameters for Virgo I finding M _ { V } = -0.33 ^ { +0.75 } _ { -0.87 } mag and r _ { h } = 47 ^ { +19 } _ { -13 } pc . Using simulations of \Lambda -dominated cold dark matter models , we predict that we should find one or two new MW satellites from \sim 300 deg ^ { 2 } HSC-SSP data , in rough agreement with the discovery rate so far . The further survey and completion of HSC-SSP over \sim 1 , 400 deg ^ { 2 } will provide robust insights into the missing satellites problem .