The quantization of the generalized mesoscopic RLC parallel circuit, the quantum fluctuations of the current and the voltage of each branch in vacuum state were studied. The influences on the quantum fluctuations of the dissipative resistances in the inductance and capacitance branches were discussed. The results show that the quantum fluctuations in each branch are related to the parameters of the elements and decay with time. The quantum fluctuations in the two branches are influenced by the dissipative resistances both in the decaying factor and in the coefficients. They have the same behavior in the decaying factor but having difference in the coefficients. The quantum fluctuations of the voltage are affected by the dissipative resistances in the two branches, but the quantum fluctuations of the current are not affected by them when the values of the two dissipative resistances are same.