Vector perturbation (VP) precoding is a promising technique to achieve near optimal capacity by exploring the channel state information (CSI) at the multiple-input multiple-output (MIMO) transmitter. To further enhance the bit error rate (BER) performance associated with forward error correction (FEC) coding, soft decision should be invoked in VP. However, the modulo operation in VP may influence the accuracy of soft decision. For alleviating this problem, the calculation of log-likelihood ratio (LLR) for VP is discussed and we further propose a sub-constellation shifted (SCS) scheme for VP precoding toward more accurate LLR. Simulation results demonstrate that the proposed scheme is capable of improving the BER performance of VP systems by accurate LLR calculation with moderate computational complexity.