We study variability of active galactic nuclei (AGNs) by using the deep optical multiband photometry data obtained from the Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) survey in the COSMOS field. The images analyzed here were taken with 8, 10, 13, and 15 epochs over three years in the g, r, i, and z bands, respectively. We identified 491 robust variable AGN candidates, down to i = 25 mag and with redshift up to 4.26. Ninety percent of the variability-selected AGNs are individually identified with the X-ray sources detected in the Chandra COSMOS Legacy survey. We investigate their properties in variability by using structure function analysis and find that the structure function for low-luminosity AGNs (L-bol less than or similar to 10(45) erg s(-1)) shows a positive correlation with luminosity, which is the opposite trend for the luminous quasars. This trend is likely to be caused by a larger contribution of the host galaxy light for lower-luminosity AGNs. Using the model templates of galaxy spectra, we evaluate the amount of host galaxy contribution to the structure function analysis and find that dominance of the young stellar population is needed to explain the observed luminosity dependence. This suggests that low-luminosity AGNs at 0.8 less than or similar to z less than or similar to 1.8 are predominantly hosted in star-forming galaxies. The X-ray stacking analysis reveals the significant emission from the individually X-ray undetected AGNs in our variability-selected sample. The stacked samples show very large hardness ratios in their stacked X-ray spectrum, which suggests that these optically variable sources have large soft X-ray absorption by dust-free gas.