The effect of the size of hurricane eye on hurricane intensity is studied based on the storm-scale kinetic energy balance within a hurricane. The study indicates that the potential intensity that a hurricane can achieve under given thermodynamic environmental conditions can be highly sensitive to the size of the hurricane eye depending on the scale of the hurricane circulation and its thermodynamic efficiency defined as the effectiveness of converting surface entropy input into kinetic energy. The result shows that a hurricane of a smaller eye tends to develop into a stronger hurricane. This is because within a hurricane, the surface kinetic energy dissipation is more radially confined to the hurricane eyewall of high wind speeds than the kinetic energy generation corresponding to the surface entropy flux mainly due to their differential dependences on the surface velocity. With a smaller eye, the area of high winds on which the dissipation relies more heavily than the surface entropy flux is smaller, implying the entire energy balance has to be achieved with a higher value of maximum surface wind. Sensitivity study on the surface exchange coefficients under high wind speeds where uncertainty exists suggests that the intensity dependence on the size of hurricane eye is not very sensitive to the uncertainty-related changes in the coefficients.