We propose a general canonical transformation for mesoscopic capacity-coupled dissipative RLC circuit and prove its feasibility and correctness. Using this transformation, the quantization of a double-loop capacity-coupled dissipation circuit is studied, and the diagonalized Hamiltonian of the system has an additional nonlinear term which has not been reported in literature. This general canonical transformation may have physical significance for the study of quantum fluctuation and quantum noise in the multiple-loop coupled dissipative circuits.