In this paper, we study the following Kirchhoff-type fractional Laplacian problem with strong singularity:... (a + b similar to u similar to 2)(- similar to)su = f ( x)u-. - k( x)uq in similar to, u > 0 in similar to, u = 0 in R3\ similar to, where (- similar to)s is the fractional Laplace operator, a, b = 0, a + b > 0, similar to is a bounded smooth domain of R3, k. L8 (similar to) is a non-negative function, q. (0, 1),. > 1 and f. L1( similar to) is positive almost everywhere in similar to. Using variational method and Nehari method, we obtain a uniqueness result. A novelty is that the Kirchhoff coefficient may vanish at zero.