With the rapid increase of access bandwidth in the next generation wireless networks, it's expected that high data rate and multimedia application will play a key role in the near future. However it's well known that the radio resource is scarce and very expensive. How to make a better utilization of the radio resource is an important research topic for future wireless communications. In this paper, we propose a tandem broadcast selective repeat (SR) ARQ scheme for high speed data communications over wireless networks. In the scheme, the base station or satellite operates in a store and forward manner, which minimizes the effect of high bit error ratio and large round trip delay in the wireless channels. Numerical results show that with a little requirement on the storage capacity in the base station or earth gateway, the proposed scheme can significantly improve the system performance.