In this paper, we consider the following fractional Kirchhoff problem with strong singularity: {(1+b∫R3∫R3|u(x)−u(y)|2|x−y|3+2sdxdy)(−Δ)su+V(x)u=f(x)u−γ,x∈R3,u>0,x∈R3,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\textstyle\\begin{cases} (1+ b\\int _{\\mathbb{R}^{3}}\\int _{\\mathbb{R}^{3}} \\frac{ \\vert u(x)-u(y) \\vert ^{2}}{ \\vert x-y \\vert ^{3+2s}}\\,\\mathrm{d}x \\,\\mathrm{d}y )(-\\Delta )^{s} u+V(x)u = f(x)u^{-\\gamma }, & x \\in \\mathbb{R}^{3}, \\\\ u>0,& x\\in \\mathbb{R}^{3}, \\end{cases} $$\\end{document} where (-Delta )^{s} is the fractional Laplacian with 0< s<1, b>0 is a constant, and gamma >1. Since gamma >1, the energy functional is not well defined on the work space, which is quite different with the situation of 0<gamma <1 and can lead to some new difficulties. Under certain assumptions on V and f, we show the existence and uniqueness of a positive solution u_{b} by using variational methods and the Nehari manifold method. We also give a convergence property of u_{b} as brightarrow 0, where b is regarded as a positive parameter.