This paper considers the application of network coding to reduce the number of retransmission by combining the lost packets from different receivers with network coding in a wireless broadcast network. In particular, the study propses an algebraic expression to define the coding conditions of retransmission packets by matrix and vector operations. According to the graph constructed by correlation matrix, an algorithm is presented to find more coding opportunity based on maximum matches in graph theory. The proposed algorithm has the ability to find the maximum pairwise coding opportunities, meanwhile, it takes into account the probability of coding the lost packets as possible to more than one retransmission packet to minimize the number of retransmissions by coding optimization, and increase the network bandwidth efficiency and throughput.