This paper deals with some Kirchhoff-type problems driven by a non-local integrodifferential operator of singular elliptic type with combined nonlinearities which generalizes the fractional Laplacian operator. Our main result is to give and prove the existence of weak solutions for such problems with homogeneous Dirichlet boundary conditions. The proof is based on a variational method, precisely, we use the Nehari manifold method and the analysis of the fibering maps.