The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a deep wide-field multi-band imaging survey consisting of three layers (Wide, Deep, and UltraDeep), with the Wide layer covering ~1470 deg^2 to a depth of i~26 mag. We present the QHSC catalog, a machine-learning selected sample of quasar candidates with photometric redshifts in the Wide layer of the HSC-SSP survey (Public Data Release 3). The full QHSC catalog contains four distinct samples: a master sample with HSC-only photometry, an HSC+WISE sample, and two samples including near-infrared data from UKIDSS and VISTA, denoted as GoldenU and GoldenV. The numbers of quasar candidates in the QHSC catalog are 1,184,574 (master), 371,777 (HSC+WISE), 87,460 (GoldenU), and 120,572 (GoldenV), with respective completeness values of 85.3%, 92.7%, 89.8%, and 91.3%. We develop ensemble photometric redshift estimators based on bootstrap aggregating (bagging) of multiple XGBoost regressors, achieving outlier fractions of 21.7%, 13.1%, 9.5%, and 10.7% for these samples. The catalog provides quasar classification probabilities (pqso), enabling construction of purer subsamples via thresholding. These four subsamples are stored as separate FITS extensions within one catalog file named "QHSC.fits".