  In this paper we study the focusing inhomogeneous 3D nonlinear Schr\"odinger
equation with inverse-square potential in the mass-supercritical and
energy-subcritical regime. We first establish local well-posedness in
$\dot{H}_a^{s_c}\cap \dot{H}_a^1$, with $s_c=3/2-(2-b)/2\sigma$. Next, we prove
the blow-up of the scaling invariant Lebesgue norm for radial solutions and
also, with an additional restriction, in the non-radial case.
