The formation of the first supermassive black holes is expected to have occurred in some most pronounced matter and galaxy overdensities in the early universe. We have conducted a submillimeter wavelength continuum survey of 54 z~6 quasars using the Submillimeter Common-User Bolometre Array-2 on the James Clerk Maxwell Telescope to study the environments around z~6 quasars. We identified 170 submillimeter galaxies (SMGs) with above 3.5{sigma} detections in 450 or 850{mu}m maps. Their far-IR luminosities are (2.2-6.4)x10^12^L_{sun}_, and their star formation rates are ~400-1200M_{sun}_/yr. We also calculated the SMGs' differential and cumulative number counts in a combined area of ~620arcmin^2^. To a 4{sigma} detection (at ~5.5mJy), SMGs' overdensity is 0.68_-0.19_^+0.21^(+/-0.19), exceeding the blank-field source counts by a factor of 1.68. We find that 13/54 quasars show overdensities (at ~5.5mJy) of {delta}_SMG_~1.5-5.4. The combined area of these 13 quasars exceeds the blank-field counts with the overdensity to 5.5mJy of {delta}_SMG_~2.46_-0.55_^+0.64^(+/-0.25) in the regions of ~150arcmin^2^. However, the excess is insignificant on the bright end (e.g., 7.5mJy). We also compare results with previous environmental studies of Ly{alpha} emitters and Lyman break galaxies on a similar scale. Our survey presents the first systematic study of the environment of quasars at z~6. The newly discovered SMGs provide essential candidates for follow-up spectroscopic observations to test whether they reside in the same large-scale structures as the quasars and search for protoclusters at an early epoch.