ABSTRACT We report the discovery of new lensed quasar candidates in the imaging data of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Data Release 4, covering $1\, 310\deg ^2$ of the sky with median seeing in the i band of ≈0.6 arcsec. In addition to two catalogues of Million Quasars Catalog v7.2 and AllWISE Catalog of Mid-Infra Red Active Galactic Nuclei, containing confirmed and candidate quasars, we preselect quasar sources using colour cuts from the HSC (grizy) and unWISE (W1 + W2) photometric data based on SDSS spectroscopic catalogues. We search for the presence of multiple point sources with similar colour through the convolution of the Laplacian of the preselected quasar image cutouts with the Laplacian of the point spread function, resulting in a reduction of lens candidates from 1 652 329 to 121 511 (7.4 per cent). After visual binary classification, we grade 6 199 (0.4 per cent) potential lenses on a scale of 0 to 3, with 3 indicating a lens and 0 indicating a non-lens. Finally we obtain 162 lens candidates with an average grade of ≥2, and among them, we successfully recover 18 known lenses. By fitting the light distribution and removing the known contaminants, we discover that 57 new systems contain at least two point sources and a galaxy in between, including 10 possible quadruply lensed quasars. This new sample exhibits a median separation of 1.26 arcsec and a magnitude limit of i ≈ 22. Spectroscopic or high-resolution imaging follow up on these newly discovered lensed quasar candidates will further allow their natures to be confirmed.