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Aiming at the deficiency that K2 algorithm depends on the maximum number of parent nodes and node of order, this paper proposed an improved Bayesian network structure learning algorithm (MWST-CS-K2). The algorithm firstly obtained the maximum number of parent nodes by constructing the maximum support tree (MWST). Then it used the correlation degree and updated coefficient between variables to set rules for adding, subtracting and reversing edges. The paper used improved cuckoo algorithm to optimize the nest location, and applied the breadth first search strategy to search and traverse to get the node order. Finally, the paper used maximum number of parent nodes and the order of nodes as the input of K2 algorithm to get the final network. Experiments show that in the standard ASIA,SACHS and CHILD network data tests, the average correct edge ratio of MWST-CS-K2 algorithm reaches 97.3%, 87.7 % and 95.6% respectively. The learning effect is better than other corresponding comparison algorithms, and the network structure obtains the most similar to the standard network structure. [ABSTRACT FROM AUTHOR]