We present the finite amplitude method (FAM) for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasi-particle-random-phase approximation (QRPA) with simple modifications. This technique has advantages over the conventional QRPA calculations, such as coding feasibility and computational cost. We perform the fully self-consistent linear-response calculation for a spherical neutron-rich nucleus 174Sn, modifying the HFBRAD code, to demonstrate the accuracy, feasibility, and usefulness of the FAM.