Let L-2 = L-2(D,rdrd theta/pi) be the Lebesgue space on the open unit disc D and let L-a(2) = L-2 boolean AND Hol(D) be a Bergman space on D. In this paper, we are interested in a closed subspace a M of L-2 which is invariant under the multiplication by the coordinate function z, and a Hankel-type operator from L-a(2) to M-perpendicular to. In particular, we study an invariant subspace M such that there does not a exist a finite-rank Hankel-type operator except a zero operator.