Chemical functionalization is an effective means to tune electronic and crystal structure of two-dimensional material, which may be crucial for moder microelectronics industry. Based on the first-principle calculation and an iterative solution of Boltzmann transport equation, we find that antimony films are potential excellent thermoelectrical materials with rather low thermal conductivities $k$ ($<$ 2.5 W/mK). The chemical functionalization can induce the reduction in $k$ to some extent, which is mainly due to the reduction of phonon lifetimes limited by the anharmonic scattering. More interesting, the origin of the reduction in $k$ is not the anharmonic interaction but the harmonic interaction from the depressed phonon spectrum mechanism, and for some chemical functional atom in halogen, the flat modes appearing in the low frequency range play also a key factor in the reduction of $k$ by significantly increasing the three-phonon scattering channels. Our work analyzes the reduction mechanism in $k$ from the chemical functionalization for antimonene, and provides a new view to adjust the thermal conductivity which can benefit thermoelectric material design.