In this article the emphasis was given to the discussion of the effects of diameter ratio and swirling on instability character for the gas/liquid coaxial jet used by Liao, et al.[1]. The results indicate that the finite diameter ratio markedly increases the maximum growth rate, the most unstable wavenumber, as well as the cutoff wavenumber. It implies that the finite diameter ratio will lead to the liquid jet breakup length shorter and the liquid drop size smaller. The effect of the swirling jets is much more complex: for the axisymmetric perturbation mode, the swirling enhances the flow stability, for helical perturbation, the dominant instability mode occurs at n<0. And it is found that in long wave region there exists a new kind of instability modes at n=1 that was not mentioned in Liao et al.’s article. For this new mode, there appears a dominated swirling ratio at which the flow has the maximum growth rate.