The linear temporal and spatial-temporal instability behavior of a confined swirling annular liquid layer was investigated theoretically. The practical situation that motivated this investigation is the core-annular film flow regime encountered in industrial heat transfer and the recessed gas-centered swirl coaxial injector, usually used in liquid propellant rocket engines. The dispersion relation for the liquid layer was developed and a parametric study was performed using this relation on the temporal and spatial-temporal instability to test the influence of non-dimensional flow parameters on the stability behavior of the layer. The temporal stability analysis shows that a larger non-dimensional outer injector radius, Rossby number, and liquid Weber number would destabilize the confined annular liquid layer. A larger liquid-to-gas density ratio and velocity ratio would decrease the disturbance growth rate. In the spatial-temporal mode, the absolute growth rate can be affected by these parameters. For a small value of liquid-to-gas density ratio, velocity ratio, and liquid Weber number, or a great value of non-dimensional radius of confinement wall and Rossby number, the flow is absolutely unstable. The wavelength predicted with spatial-temporal analysis is much larger than that predicted using the temporal analysis. However, the wavelength rarely changes with these dimensionless parameters in absolute instability mode.