Deep space networks, satellite networks, ad hoc networks, and the Internet can be modeled as DTNs (Delay Tolerant Networks). As a fundamental problem, the maximum flow problem is of vital importance for routing and service scheduling in networks. However, there exists no permanent end-to-end path since the topology and the characteristics of links are time-variant, resulting in a crucial maximum flow problem in DTNs. In this paper, we focus on the single-source-single-sink maximum flow problem of buffer-limited DTNs, followed by a valid algorithm to solve it. First, the BTAG (Buffer-limited Time Aggregated Graph) is constructed for modeling the buffer-limited DTN. Then, on the basis of BTAG, the two-way cache transfer series and the relevant transfer rules are designed, and thus a BTAG-based maximum flow algorithm is proposed to solve the maximum flow problem in buffer-limited DTNs. Finally, a numerical example is given to demonstrate the effectiveness of the proposed algorithm.