We report theoretical results for the $\Omega_c(3120)$ state, observed by the LHCb collaboration, based on the molecular picture. The mass of the $\Omega_c(3120)$ state is reproduced from the $s$-wave $\Xi^*_c \bar K$ and $\Omega^*_c \eta$ channels. The width of the $\Omega_c(3120)$ is reproduced by introducing the $d$-wave $\Xi_c \bar{K}$ channel in addition to the other two channels. Furthermore, we calculate the partial decay widths of the $\Omega_c(3120)$ into $\Xi_c \bar{K}$ and $\pi \Xi_c \bar{K}$, following a discussion on the molecular nature of the $\Omega(2012)$ state. We find that the scattering length and effective range, along with the binding energy and width of the $\Omega_c(3120)$ state, can provide useful information for discussing the nature of the $\Omega_c(3120)$ state in the near future.