The invention relates to a low-dielectric-constant liquid crystal polymer composition and a preparation method thereof. The low-dielectric-constant liquid crystal polymer composition is prepared fromthe following raw materials: liquid crystal polymer A resin, liquid crystal polymer B resin, hydrogenated styrene-butadiene-styrene copolymer grafted maleic anhydride, hollow glass beads, a polyhedraloligomeric silsesquioxane polymer, a titanate coupling agent, polytetrafluoroethylene resin, a hyperbranched polyester polymer, erucyl amide, N, N-dimethylacetamide, N-dimethylacetamide, N-dimethylacetamide, N-dimethylacetamide, N-dimethylacetamide, N-dimethylacetamide and the like. According to the composition, N, N '-bis (2, 2, 6, 6-tetramethyl-4-piperidyl)-1, 3-benzenedicarboxamide and bis (2,6-di-tert-butyl-4-methylphenyl) pentaerythritol diphosphate are used as raw materials. The low-dielectric-constant liquid crystal polymer composition has excellent mechanical properties, processability and low dielectric constant, and can be applied to shells, cladding and protective materials and the like of 5G base stations, micro base station systems, data communication terminals, antennas andradio frequency modules.