By using the technique of integration within ordered product (IWOP) of operators, the time-evolution operator can be expressed as quantum image of the classical transformation in the coordinate and momentum phase space. The quantized mesoscopic RLC (resistance, capacitance and inductance) electric circuit and the corresponding Hamiltonian were obtained according to the way of the quantized mesoscopic LC electric circuit. By means of theoretical calculations, it was shown that there exists squeezing mechanism in the quantized mesoscopic RLC electric circuit. Furthermore, the concrete form of the squeezed state in the quantized mesoscopic RLC electric circuit was derived based on the IWOP technique and quantum Fresnel transformation.