Studies of spatial distribution, kinematics, and physical structure of dense molecular gas in the centers of galaxies is crucial in understanding the nature of physical processes, especially those related to active galactic nuclei (AGNs) and starbursts, in the vicinity of central massive black holes. However, our current understanding of dense gas in the circumnuclear disks (CND) remains limited, particularly those around AGNs. Here we report high-resolution deep observations of the CS (3-2), HC3N (15-14), H2CO (2-1), CH3CCN (8-7), CO (1-0), and (3-2) lines, toward the central region (R ∼ 0.4 kpc) of the nearest Seyfert-2 galaxy, the Circinus galaxy, using the Atacama Large Millimeter/submillimeter Array (ALMA). The dense molecular gas traced by CS (3-2) and HC3N (15-14) exhibit an asymmetric and cloud structure, which is in sharp contrast against the symmetric low-density structure traced by CO (1-0). Four molecular cloud structures surrounding the AGN, which have a typical size of ∼ 20 pc, are detected with the optically thin HC3N (15-14) line. HC3N (15-14)/CO (1-0) line ratio in the circumnuclear disk is found to be higher than that in the nuclear region, indicating that the bulk of dense gas accumulates in the CND, instead of the nucleus. HC3N (15-14) line and optically thick tracers in four molecular clouds, provide a good comparison between density layers and show evidence for a density stratification of the CND.