In this paper, we propose a transmission scheme to enhance the uplink throughput for wireless sensor networks (WSNs). Different from most existing approaches, the proposed approach requires no changes in the hardware structure of the low power and distributed sensor nodes (SNs). Instead, the central node (CN), which knows the channel state information, assigns to each SN a properly selected starting time for transmission. A portion of the received signals from different SNs at the CN is overlapped and hence non-orthogonal. However, this can be recovered by an iterative detection/decoding algorithm. Numerical results show that the proposed scheme performs well under large-scale fading and/or small-scale fading channels. Compared with the traditional non-overlapping transmission scheme, the proposed scheme improves the uplink throughput under various channel conditions without extra transmission power consumption.