Tsallis-q entanglement is a well-known entanglement measures which obeys a tighter monogamy inequality with q∈[2,3]. We extend the range of q for analytic formula of Tsallis-q entanglement to q∈[(5-√13)/2,(5+√13)/2], and prove that it is a tighter monogamy inequality of quantum entanglement in terms of squared Tsallis-q entanglement. It is tighter than existing ones,and the range of q become broader than tighter monogamy inequality using Tsallis-q entanglement.