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Low duty cycled sleep scheduling can largely prolong the lifetime of a wireless sensor network (WSN). However, it also brings big challenge to the design of efficient routing protocols. Inappropriate selection of routes can largely offset the efficiency of a sleep scheduling mechanism. This paper aims to provide a simple but efficient forwarding discipline for packet routing in a low duty cycled WSN wherein each node chooses its wakeup slot in a pseudo-random manner. In such a duty-cycled WSN, a big problem is how a node can make a forwarding decision in order to obtain an acceptable end-to-end (E2E) delivery latency as well as high energy efficiency. In this paper, we design a multipath routing protocol that combines gradient information and predictable link delay to make the forwarding decision. Simulation results show that the designed protocol can obtain high performance in terms of delivery latency and energy efficiency compared with existing work.