For a compact Kähler manifold, by considering the high tensor powers of a prequantum line bundle, Shiffman and Zelditch (1999) proved the equidistribution of the zeros of random holomorphic sections in the context of semiclassical limit. There are already many generalizations and extensions of this result in various geometric or probabilistic settings, in particular, the large deviation estimate and hole probability were obtained for compact Hermitian manifolds. In this talk, I would like to present a generalization of these results to the case of noncompact complex manifolds. We start with the construction of the Gaussian-like random holomorphic sections for Hermitian holomorphic line bundles on a noncompact Hermitian complex manifold. We are particularly interested in the case where the space of square integrable holomorphic sections is infinite dimensional. Then we study their random zeros in the context of semiclassical limit, including the equiditribution, the large deviation estimate and the hole probability. This talk is based on the joint work with  Alexander Drewitz and George Marinescu.