[Li Xin] Chinese Acad Sci, Inst Theoret Phys, Beijing 100190, Peoples R China
; [Chang Zhe] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; [Mo Xiao-Huan] Peking Univ, Sch Math Sci, Key Lab Pure & Appl Math, Beijing 100871, Peoples R China
; [Li Xin
; Chang Zhe] Chinese Acad Sci, Theoret Phys Ctr Sci Facil, Beijing 100049, Peoples R China
We present an explicit connection between the symmetries in a Very Special Relativity (VSR) and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR, are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR, are discussed.