Due to the rapid development of quantum computing and quantum information, the physical study of solid-state quantum systems has revived significant interest. Among the possible schemes for the experimental realization of quantum computing, mesoscopic circuits containing small solid-state devices have attracted much attention, because of their advantages of easy integration and large-scale characteristics. Since the actual mesoscopic circuit is always in a certain environment, it is inevitably affected by the environment. For example, a mesoscopic circuit is radiated by an external electromagnetic field. The transitions will occur between different energy levels of the system. It is valuable to find the rules of energy level transition. In this paper, a more general mesoscopic LC circuit with complex coupling is chosen as the research object. By virtue of the canonical quantization method, the mesoscopic circuit is quantized and the Hamiltonian operator of the system is obtained. With the help of unitary transformation and analogy with a one-dimensional quantum harmonic oscillator, it is found that the mesoscopic LC circuits with complex couplings can be considered as two independent quantum mechanical harmonic oscillators. Then, the energy level formula and state vector expression of the system are deduced easily. In addition, the mean square quantum fluctuations, in the ground state, of the charges on one plate of the capacitor in the two branches of the mesoscopic circuit, and the equivalent magnetic flux passing through the two loops, are discussed. Considering that, once the mesoscopic circuit is irradiated by the external electromagnetic field, its state will change and a transition between the corresponding energy levels will occur. By using the “invariant Eigen-operator” method, the selection rules of energy-level transition for the mesoscopic LC circuit with complex couplings are obtained conveniently. It is believed that the application of this methodwill enrich the theoretical research on mesoscopic circuit from a fresh point of view.