Reed-Muller (RM) sequences have been widely used in compressed sensing (CS) to construct deterministic measurement matrices and extract attributes of sparse signals. However, if the signal is not sparse enough, the existing reconstruction algorithms encounter serious performance degradation. In this paper, invoking the elegant nested structure of second-order RM sequences, a soft-decision reconstruction algorithm is proposed. With the soft- information passing through the nested structure, the proposed reconstruction algorithm outperforms the existing ones. Notably, the performance can be further improved based on shuffling operations. Numerical results verify the good performance of the proposed algorithm and show that it preserves quite low computational complexity.