We present new measurements of the quasar luminosity function ( LF ) at z \sim 6 , over an unprecedentedly wide range of the rest-frame ultraviolet luminosity M _ { 1450 } from -30 to -22 mag . This is the fifth in a series of publications from the Subaru High- z Exploration of Low-Luminosity Quasars ( SHELLQs ) project , which exploits the deep multi-band imaging data produced by the Hyper Suprime-Cam ( HSC ) Subaru Strategic Program survey . The LF was calculated with a complete sample of 110 quasars at 5.7 \leq z \leq 6.5 , which includes 48 SHELLQs quasars discovered over 650 deg ^ { 2 } , and 63 brighter quasars discovered by the Sloan Digital Sky Survey and the Canada-France-Hawaii Quasar Survey ( including one overlapping object ) . This is the largest sample of z \sim 6 quasars with a well-defined selection function constructed to date , and has allowed us to detect significant flattening of the LF at its faint end . A double power-law function fit to the sample yields a faint-end slope \alpha = -1.23 ^ { +0.44 } _ { -0.34 } , a bright-end slope \beta = -2.73 ^ { +0.23 } _ { -0.31 } , a break magnitude M _ { 1450 } ^ { * } = -24.90 ^ { +0.75 } _ { -0.90 } , and a characteristic space density \Phi ^ { * } = 10.9 ^ { +10.0 } _ { -6.8 } Gpc ^ { -3 } mag ^ { -1 } . Integrating this best-fit model over the range -18 < M _ { 1450 } < -30 mag , quasars emit ionizing photons at the rate of \dot { n } _ { ion } = 10 ^ { 48.8 \pm 0.1 } s ^ { -1 } Mpc ^ { -3 } at z = 6.0 . This is less than 10 % of the critical rate necessary to keep the intergalactic medium ionized , which indicates that quasars are not a major contributor to cosmic reionization .