Making use of the invariant property of the equilibrium size distribution of the hydrogen bonding clusters formed in hydrogen bonding system of AaDd type, the analytical expressions of the free energy in pregel and postgel regimes are obtained. Then the gel free energy and the scaling behavior of the number of hydrogen bonds in gel phase near the critical point are investigated to give the corresponding scaling exponents and scaling law. Meanwhile, some properties of intermolecular and intramolecular hydrogen bonds in the system, sol and gel phases are discussed. As a result, the explicit relationship between the number of intramolecular hydrogen bonds and hydrogen bonding degree is obtained.