Superhydrophobic surfaces have attracted great interest due to their self-cleaning, dust-proofing and friction-reducing properties. Related papers have proposed methods and theoretical bases for preparing these surfaces in order to achieve excellent superhydrophobicity. However, the influence of the roughness of the solid surface structure on its superhydrophobicity requires further in-depth thermodynamic analysis. In this paper, three-dimensional (3D) cylinder microtextured surface models are selected based on thermodynamic analysis. On this basis, a simulation diagram of the three-phase contact line of a circular cylinder section in a 3D model is presented. The effects of the intrinsic contact angle and geometrical parameters of the cylinder microtexture on free energy and the free energy barrier, as well as contact angle hysteresis, are theoretically investigated. The obtained results reveal the necessity of the transition between the non-composite state and composite state. The transition criteria between the non-composite and composite wetting states are obtained from the perspective of thermodynamic analysis and theoretical equations. The calculated results are basically consistent with the theoretical calculations and experimental results. This method provides theoretical guidance for the design of superhydrophobic surfaces.