Sparse vector coding (SVC) is a promising short-packet transmission method for ultra reliable low latency communication (URLLC) in next generation communication systems. In this paper, a dual-mapping SVC (DM-SVC) based short packet transmission scheme is proposed to further enhance the transmission performance of SVC. The core idea behind the proposed scheme lies in mapping the transmitted information bits onto sparse vectors via block and single-element sparse mappings. The block sparse mapping pattern is able to concentrate the transmit power in a small number of non-zero blocks thus improving the decoding accuracy, while the single-element sparse mapping pattern ensures that the code length does not increase dramatically with the number of transmitted information bits. At the receiver, a two-stage decoding algorithm is proposed to sequentially identify non-zero block indexes and single-element non-zero indexes. Extensive simulation results verify that proposed DM-SVC scheme outperforms the existing SVC schemes in terms of block error rate and spectral efficiency.