Existing duty-cycling and pipelined-forwarding (DCPF) protocols applied in battery-powered wireless sensor networks can significantly alleviate the sleep latency issue and save the energy of networks. However, when a DCPF protocol applies to a linear sensor network (LSN), it lacks the ability to handle the bottleneck issue called the energy-hole problem, which is mainly manifested due to the excessive energy consumption of nodes near the sink node. Without overcoming this issue, the lifespan of the network could be greatly reduced. To that end, this paper proposes a method of deploying redundant nodes in LSN, and a corresponding enhanced DCPF protocol called redundancy-based DCPF (RDCPF) to support the new topology of LSN. In RDCPF, the distribution of energy consumption of the whole network becomes much more even. RDCPF also brings improvements to the network in terms of network survival time, packet delivery latency, and energy efficiency, which have been shown through the extensive simulations in comparison with existing DCPF protocols.