In this paper, we focus on end-to-end transfer delay improvement by using erasure coding when delivering expediting message consisting of M packets in networks with high coefficient of variation of transfer time. In the scheme, M packets are divided into b groups with each having g packets. Each group is erasure coded with additional r packets and transmitted. Since the first arrived g packets among g+r packets completes the delivery of the group, the delivery time of the expediting message is reduced. For the scheme, we investigate the optimum group size and number of redundancy packets considering delivery delay reduction and additional transmission cost caused by using erasure coding. From the results of the investigation, we see that the proposed scheme is effective in networks having high variability of transfer time and would be very useful and practical especially for the case that expedited deliveries of messages are needed.