“Minimizing path delay” is one of the challenges in low Earth orbit (LEO) satellite network routing algo-rithms. Many authors focus on propagation delays with the distance vector but ignore the status information and processing delays of inter-satellite links. For this purpose, a new discrete-time traffic and topology adap-tive routing (DT-TTAR) algorithm is proposed in this paper. This routing algorithm incorporates both inher-ent dynamics of network topology and variations of traffic load in inter-satellite links. The next hop decision is made by the adaptive link cost metric, depending on arrival rates, time slots and locations of source-destination pairs. Through comprehensive analysis, we derive computation formulas of the main per-formance indexes. Meanwhile, the performances are evaluated through a set of simulations, and compared with other static and adaptive routing mechanisms as a reference. The results show that the proposed DT-TTAR algorithm has better performance of end-to-end delay than other algorithms, especially in high traffic areas