Abstract: Rayleigh-Taylor instability is one of the classical problems in fluid mechanics, which is widely used in underwater explosions, droplet formation, liquid sprays, and other engineering applications. The interfacial instability of cylindrical droplet induced by a cavitation bubble is one of the classical models in its study. As the perturbation of the interfacial instability develops, three distinct characteristics of the droplet deformation are obtained: (i) a splashing state; (ii) a ventilating state; and (iii) a stable state. Considering that liquid viscosity is an important factor affecting the development of interfacial instability, the influence of liquid viscosity on the interfacial instability of a cylindrical droplet induced by a cavitation bubble is investigated through a high-precision numerical simulation method in this paper. A direct numerical simulation is set up based on the compressible multiphase solver in the OpenFOAM framework. The interfaces are captured using a geometric fluid volume method named isoAdvector. The results show that within the parameters discussed in the paper, an increase in liquid viscosity slows down the oscillation of the bubble, thus reducing the perturbation growth rate during the bubble collapse. In these cases, the onset time of ventilation increases for a ventilating state, and the maximum perturbation reduces for a stable state. This reduction directly affects the distinct characteristics of the droplets. A phase diagram of the interfacial instability of droplets with different initial radius and liquid viscosity is obtained based on the results of numerical simulations. With the increase of liquid viscosity, the small droplets (R_d0 < 2 mm) change from a splashing state to a ventilating state and then a stable state; the medium droplets (2 mm < R_d0 < 3 mm) change from a ventilating state to a stable state; whereas, the large droplets (R_d0 > 3 mm) does not change and stay only in a stable state. The droplet tends to stabilize as the liquid viscosity increases.