Abstract: Marangoni convection induced by surface tension gradient along the liquid of finite thickness was researched. It is assumed that the surface tension is a quadratic function of temperature, the under surface temperature is constant, and the super surface temperature is a linear function of horizontal distance. The Marangoni convection boundary layer problem was solved by an efficient transformation and asymptotic expansion technique, and the analytical approximate solution to this Marangoni convection was obtained. The effects of Marangoni number and Prandtl number on the velocity and temperature boundary layers were discussed and the associated transfer mechanism was analyzed in detail.