In the soft-input soft-output Viterbi algorithm (SOVA), the log-likelihood ratio (LLR) of each bit is determined by the minimum metric difference between the ML path and its competitive paths. This paper proposes to trim large metric differences in order to reduce the complexity of SOVA. By trimming the metric differences, only a small number of backtracking operations are carried out, while many LLRs may be omitted as the result of the lack of metric differences. By revealing the relationship among neighboring LLRs, the omitted LLRs are estimated from its neighoring LLRs as well as intrinsic information. The extrinsic information transfer chart analysis demonstrates that the proposed algorithm has similar convergence behavior as the Log-MAP algorithm, if the trimming factor M is moderate. Other analyses verify that our approach provides good LLR quality with only at most 1/M backtracking operations of SOVA. Simulation results show that it outperforms SOVA and performs as well as its variants and the Log-MAP algorithm.