The exact solution of time evolution of quantum state in the mesoscopic LC circuit driven by a time dependent source were obtained by applying the Wei-Norman method. The quasi-probability distribution functions of phase space was used to investigate the quantum state of the mesoscopic LC circuit in coherent state. The results show that the function of the system is two dimension motional Gauss wave-packet. The centre charge and flux of the wave-packet vary with cosine and sine wave.