The temporal mode stability of incompressible submerged axisymmetric gas jets is comprehensively investigated by linear stability analysis. The basic velocity profile is constructed using the hyperbolic tangent function approach. The influences of basic velocity profile, Reynolds Re, and Weber We numbers, and physical properties of the surrounding liquid on the stability of the gas jet are investigated and stability maps are constructed. We find that the jet breakup propagation velocity shows a strong linear relationship with the velocity of the two-phase interface, and the shear on the interface can greatly change the instability modes of submerged gas jet system. Large surface tension triggers long-wave instability of the jet and local shear at the interface leads to the unsteady transition to short-wave instability. Moreover, it is found that there is a strong linear relationship between the most unstable growth rate and dimensionless parameters directly or indirectly, and R-2 is above 0.95. In addition, the instability of the submerged gas jet shows a double-mode feature when the velocity profile parameters exceed their thresholds.