The equation of the state of the hydrogen bonding fluid system of AaDd type is studied by the principle of statistical mechanics. The influences of hydrogen bonds on the equation of state of the system are obtained based on the change in volume due to hydrogen bonds. Moreover, the number density fluctuations of both molecules and hydrogen bonds as well as their spatial correlation property are investigated. Furthermore, an equation describing relation between the number density correlation function of "molecules-hydrogen bonds" and that of molecules and hydrogen bonds is derived. As application,taking the van der Waals hydrogen bonding fluid as an example, we considered the effect of hydrogen bonds on its relevant statistical properties.