In wireless multicast,network coding has recently attracted attentions as a substantial improvement to packet retransmission schemes.However,the problem of finding the optimal network code which minimizes the retransmissions is hard to solve or approximate.This paper presents two schemes to reduce the number of retransmissions for reliable multicast efficiently.One is retransmission using network coding based on improved Vandermonde matrix (VRNC),the other is retransmission using network coding based on adaptive improved Vandermonde matrix (AVRNC).Using VRNC scheme the sender selects the packets all receivers have lost and encodes them with improved Vandermonde matrix; when receivers receive enough encoded retransmission packets,all the lost packets can be recovered.With AVRNC scheme,the sender can obtain the recovery information from all the receivers after sending out per retransmission packet,and then the improved Vandermonde matrix can be updated,thus reducing the complexity of encoding and decoding.Our proposed schemes can achieve the theoretical lower bound assuming retransmission packets lossless,and approach the theoretical lower bound considering retransmission packets loss.Simulation results show that the proposed algorithms can efficiently reduce the number of retransmissions,thus improving transmission efficiency.