A temporal linear stability analysis has been carried out to predict the instability of a viscous liquid jet surrounded by a swirling air stream with three-dimensional disturbances. The effects of flow conditions and fluid properties on the instability of the liquid jet are investigated via a parametric study by varying axial Weber number axial velocity ratio of the gas to liquid phase, swirl Weber numbers, density ratio and the Ohnesorge number. It is observed that the relative axial velocity between the liquid and gas phases promotes the interfacial instability. As the axial Weber number increases, the growth rates of unstable waves, the most unstable wavenumber and the unstable range of wavenumbers increase. Meanwhile, the increasing importance of helical modes compared to the axisymmetric mode switches the breakup regime from the Rayleigh regime to the first wind-induced regime and on to the second wind-induced regime. The predicted range of wavenumbers in which the first helical mode has higher growth rates than the axisymmetric mode agrees very well with experimental data. Results show that the destabilizing effects of the density ratio and the axial Weber number are nearly the same. Liquid viscosity inhibits the disintegration process of the liquid jet by reducing the growth rate of disturbances and by shifting the most unstable wavenumber to a lower value. Moreover, it damps higher helical modes more significantly than the axisymmetric mode. Air swirl has a stabilizing effect on the liquid jet. As air swirl strength increases, the growth rates of helical modes are reduced more significantly than that of the axisymmetric mode. The air swirl profile is found to have a significant effect on the instability of the liquid jet. The global, as well as local, effects of the swirl profile are examined in detail.