We apply a novel model based on convolutional neural networks (CNN) to identify gravitationally-lensed galaxies in multi-band imaging of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Survey. The trained model is applied to a parent sample of 2 350 061 galaxies selected from the ∼ 800 deg2 Wide area of the HSC-SSP Public Data Release 2. The galaxies in HSC Wide are selected based on stringent pre-selection criteria, such as multiband magnitudes, stellar mass, star formation rate, extendedness limit, photometric redshift range, etc. The trained CNN assigns a score from 0 to 1, with 1 representing lenses and 0 representing non-lenses. Initially, the CNN selects a total of 20 241 cutouts with a score greater than 0.9, but this number is subsequently reduced to 1 522 cutouts after removing definite non-lenses for further visual inspection. We discover 43 grade A (definite) and 269 grade B (probable) strong lens candidates, of which 97 are completely new. In addition, we also discover 880 grade C (possible) lens candidates, 289 of which are known systems in the literature. We identify 143 candidates from the known systems of grade C that had higher confidence in previous searches. Our model can also recover 285 candidate galaxy-scale lenses from the Survey of Gravitationally lensed Objects in HSC Imaging (SuGOHI), where a single foreground galaxy acts as the deflector. Even though group-scale and cluster-scale lens systems are not included in the training, a sample of 32 SuGOHI-c (i.e., group/cluster-scale systems) lens candidates is retrieved. Our discoveries will be useful for ongoing and planned spectroscopic surveys, such as the Subaru Prime Focus Spectrograph project, to measure lens and source redshifts in order to enable detailed lens modelling.