Using a simple analytic approach, we study the universal properties of second-order phase transition in holographic superconductor models. We explore a general model in arbitrary dimensions in which the condensation occurs via the Stuckelberg spontaneous symmetry breaking mechanism. All the possible second-order phase transitions and their universal characteristics can be identified analytically. The relationship between the critical temperature and charge density is generic, and the critical exponents can be greater than the typical mean field value 1/2. In addition, the related numerical factors can also be computed qualitatively.