Mobile data traffic increased rapidly due to the spread of mobile devices such as smartphones and tablets. Therefore, the technology of efficiently transmitting data have become indispensable for base stations to serve a large amount of traffic in time. Multicasting is one of the representative scheme to transmit data efficiently when transmitting the same data for many users. Many papers have studied multicasting for simultaneous user requests. In this paper, we consider multicasting for asynchronous request for multiple users case. We propose a multicasting scheme to merge the multiple unicast transmission into multicast transmission by grouping the users who request the same file during “set-up time”. Through analyzing the mathematical model of our proposed scheme, we suggest the algorithm to find joint optimal pair of rate and set-up time to minimize average transmission time for group users. In conclusion, we confirmed that unicast merging could reduce the average transmission time of users in a group.