Atomic carbon (CI) has a great potential for estimating cold molecular gas mass as an alternative to low-J CO, especially in high redshift galaxies or metal-poor objects. The distribution of CI and relation between CI and CO, however, have not yet been fully understood. We carried out observations toward the central region of a nearby Seyfert galaxy NGC~613 in [CI]($^3P_1-^3P_0$), $^{13}$CO, and C$^{18}$O($J=1-0$) with ALMA. The circum-nuclear disk (CND) and star forming ring were found by the lines. The distribution of [CI] in the ring resembles that of the CO emission, although [CI] is prominent in the CND. This can be caused by the low intensities of the CO isotopes due to the low optical depths under the high temperature in the CND. We found that the intensity ratios of [CI] to $^{12}$CO(3--2) ($R_{¥rm CI/CO}$) and to $^{13}$CO(1--0) ($R_{¥rm CI/^{13}CO}$) are high at several positions around the edge of the ring. The spectral profiles of the CO lines mostly correspond each other both in the ring and at spots of high $R_{¥rm CI/CO}$, but the profile of [CI] is different from CO at the high $R_{¥rm CI/CO}$. These results indicate that [CI] at the high $R_{¥rm CI/CO}$ traces different gas from that traced by the CO lines. In addition, the [CI] kinematics along the minor axis of NGC~613 could be interpreted as a bubbly molecular outflow. The outflow rate of molecular gas is higher than star formation rate in the CND. The flow could be mainly boosted by the AGN through its radio jets.