The convective heat transfer with constant heat flux condition inside a circular microchannel was investigated. The velocity and temperature profiles with a slip velocity at the surface were derived，and then the heat transfer coefficient and Nusselt number were obtained. A model was proposed for effective conduction at the super-hydrophobic surface with different structural parameters and the thermal resistance of the surface with trapped air was calculated. The effective heat transfer coefficient of super-hydrophobic surface was related to the heat transfer coefficient and surface thermal resistance. The calculation gives the following results. The slip of fluid on a super-hydrophobic surface makes the temperature profile inside the channel more uniform，so that the heat transfer coefficient or Nusselt number is increased，which may reach 2. 8 times that without slip under constant heat flux condition. The thermal resistance of super-hydrophobic surface increases with trapped air volume. The effective heat transfer coefficient on super-hydrophobic surface declines seriously as the trapped air volume increases，especially as the trapped air area at the surface increases. There exists a critical thickness for the trapped air on the super-hydrophobic surface with given surface structural parameters，under which the effective heat transfer coefficient is not less than that on general surfaces without slip. Therefore，it is necessary to adopt appropriate structure for the surface，such as rib height and distance between ribs，to avoid trapping air，so that the heat transfer on the super-hydrophobic surface is enhanced.