In this paper, we study the geometry of indefinite generalized Sasakian space form $ar{M}(f_1, f_2, f_3)$ admitting a lightlike hypersurface $M$ subject such that the almost contact structure vector field $zeta$ of $ar{M}(f_1, f_2, f_3)$ is tangent to $M$. We prove a classification theorem of such an indefinite generalized Sasakian space form.

Keywords: indefinite generalized Sasakian space form,indefinite trans-Sasakian manifold, lightlike hypersurface