A temporal stability analysis has been carried out to model the breakup of a power-law liquid jet. The dispersion relation of a power-law liquid jet is obtained by integrating the axisymmetric governing equations for the power-law liquid jet. The effects of the surface tension, liquid jet radius, air boundary layer, liquid consistency coefficients, gas dynamic viscosity, power-law index, and the relative velocity between the liquid and gas phase on the maximum growth rate and the dominant wave number are studied. The investigation shows that the maximum growth rate and the dominant wave number increase with the increase of the relative velocity and gas dynamic viscosity, while they both decrease as the liquid surface tension, liquid jet radius, air boundary layer, and power-law index increase. Therefore, increasing the relative velocity and gas dynamic viscosity, or decreasing the liquid surface tension, liquid jet radius, air boundary layer, liquid consistency coefficient, or power-law index will improve the instability of the liquid jet and be advantageous for the breakup of the liquid jet. The liquid consistency coefficient on liquid jet instability has a critical value, and the low liquid consistency coefficient will make the jet more unstable.