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For a mesoscopic L-C circuit, besides the Louisells quantization scheme in which electric charge q and electric current Ⅰ are respectively quantized as the coordinate operator Q and momentum operator P, in this paper we propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The comparison between this number-phase quantization with the Josephson junctions Cooper pair numberphase-difference quantization scheme is made.