The theoretical research of circular liquid jets disintegration is very important for the study on the science of engine atomization and combustion. The linear stability theory is an important method for studying on disintegration process of circular liquid jets. This paper reports a linear stability analysis for a viscous circular liquid jet moving in a incompressible gas medium. Derivation employs the linearized Navier?Stokes dimensionless equations, the dimensionless linearized kinematic and dynamic boundary conditions of liquid and gas phases. Meanwhile, applying the dot product of the gradient operator ▽with momentum equation method, a n?order dimensionless dispersion relation is obtained.