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General Bayesian network classifier (GBNC) contains only features necessary for classification, so an ideal structure learning solution is to learn GBNC without having to learn the whole Bayesian network (BN). A local search based algorithm called LAS-GBNC is proposed. Given faithfulness assumption, LAS-GBNC relies on the information about each variable's appearance in the so-called d-separator(cut set) to sort candidate CI tests dynamically, performing `effective' ones with priority. Experimental studies indicate that (1) LAS-GBNC achieves the same quality of networks as PC and IPC-BNC, (2)It is much more efficient than PC due to its local search design, and (3) It is obviously faster than IPC-BNC because of its adaptive search strategy.