ABSTRACT Recent studies show that a universal relation between black hole (BH) growth and stellar mass (M⋆) or star formation rate (SFR) is an oversimplification of BH–galaxy coevolution, and that morphological and structural properties of host galaxies must also be considered. Particularly, a possible connection between BH growth and host-galaxy compactness was identified among star-forming (SF) galaxies. Utilizing ≈6300 massive galaxies with I814W  <  24 at z < 1.2 in the Cosmic Evolution Survey (COSMOS) field, we perform systematic partial correlation analyses to investigate how sample-averaged BH accretion rate ($\rm \overline{BHAR}$) depends on host-galaxy compactness among SF galaxies, when controlling for morphology and M⋆ (or SFR). The projected central surface mass density within 1 kpc, Σ1, is utilized to represent host-galaxy compactness in our study. We find that the $\rm \overline{BHAR}$–Σ1 relation is stronger than either the $\rm \overline{BHAR}$–M⋆ or $\rm \overline{BHAR}$–SFR relation among SF galaxies, and this $\rm \overline{BHAR}$–Σ1 relation applies to both bulge-dominated galaxies and galaxies that are not dominated by bulges. This $\rm \overline{BHAR}$–Σ1 relation among SF galaxies suggests a link between BH growth and the central gas density of host galaxies on the kpc scale, which may further imply a common origin of the gas in the vicinity of the BH and in the central ∼kpc of the galaxy. This $\rm \overline{BHAR}$–Σ1 relation can also be interpreted as the relation between BH growth and the central velocity dispersion of host galaxies at a given gas content (i.e. gas mass fraction), indicating the role of the host-galaxy potential well in regulating accretion on to the BH.