Frequent itemsets (FIs) mining is the main challenge in analyzing association rules since the complexity of association rule mining is determined mainly by identifying all frequent itemsets. There are many approaches to FIs mining; each approach includes many algorithms, but there is a major weakness in the logic-design-based FIs approach because there is a limited number of methods for logic circuit or expression optimization, each of which suffers from some drawbacks that are transferred to the mining process when they are utilized for this purpose. We propose LCOFI, a new algorithm for frequent itemset mining based on the LCO algorithm, in this paper. LCOA is a new algorithm for logic circuit optimization. LCOFI utilizes the suggested operations for a bipartite graph in LCOA. The proposed algorithm is simple and efficient and supports a large number of input items. It scans the transaction database only once to construct the bipartite graphs of frequent 1-itemsets and avoids the generation of candidate itemsets. It does not require complex data structures such as trees and hash tables to validate the frequency of FIs. When applied to a variety of datasets with varying characteristics, the proposed algorithm, LCOFI, outperformed the Apriori and Fp-growth algorithms in all the experiments.