The study object in this article is a laminar aerofoil, which belongs to a high altitude long endurance UAV with big wing aspect ratio. With the help of advanced technology of computation fluid dynamics (CFD), genetic algorithms are combined with N-S equations for the aerofoil optimization design at the bound of low Reynolds number to perform the aerodynamic shape optimization design of aerofoil. The aerofoil is described by equations of linearity adding analytic Hicks-Henne shape function on the basis of original aerofoil. The individual is formatted by variables of the linearity adding analytic functions, by the program of selection, crossover and variance, the aerofoil is optimized with the purpose of rising lift-drag ratio. As a result, there is an increase of lift-drag ratio and life coefficient of the optimized aerofoil at low Reynolds number. The optimization results illustrate that the genetic algorithms are of an effective way for the optimization design of aerofoil.