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Based on the Navier-Stokes equation,an equation describing the Langmuir circulation is derived by a perturbation method when the influences of Coriolis force and buoyancy force are both considered.The approach used in the analysis is similar to the works carried out by Craik and Leibovich[J.Fluid Mech.73 (1976)401],Leibovich [J.Fluid Mech.79 (1977) 715]and Huang[J.Fluid Mech.91 (1979) 191].Potential applications of the equation proposed are discussed in the area of Antarctic circumpolar current.