Using number-phase quantization scheme, mesoscopic LC circuit is quantized to one dimensional harmonic oscillator coupled to a thermal field. The Wigner function of the free thermal state is obtained by using the coherent state representation and normal product form of operators, and then the quantum effects of charge number and phase-difference in free thermal state are discussed by using Weyl-Wigner correspondence. It is found that, the quantum fluctuations of charge number and phase-difference in free thermal state are related to not only the parameters of the circuit, but also the temperature, and the average energy stored in the capacitance and inductance is equal to each other. It is proven that the number-phase quantization is very useful to tackle with quantization of some mesoscopic circuits and the quantum effects.