In this letter, a new approximation of log-likelihood ratio (LLR) for soft input channel decoding is proposed. Conventional simplified LLR using log-sum approximation can degrade the performance of bit interleaved coded modulation (BICM) systems employing hybrid automatic repeat request (HARQ) at low SNR. The proposed LLR performs as well as the exact LLR, and at the same time, requires only a small number of elementary operations.