We show that every hyperbolic manifold of finite volume and dimension greater or equal to 3 is stable under normalized Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Here we do not need to make any decay assumptions on this perturbation. As we will see, the main difficulty in the proof comes from a weak stability of the cusps which has to do with the existence of certain cusp deformations. We will overcome this weak stability by using a new analytical method developed by Koch and Lamm.