In this paper a log-MAP turbo decoding algorithm which incorporates reliability threshold based trellis branch elimination together with mean based early iteration termination has been proposed. The proposed algorithm reduces computational complexity by eliminating branches in trellis. Since the minimum Log Likelihood Ratio (LLR) obtained for each iteration varies with channel conditions, an early iteration termination based on the mean of extrinsic information has been combined with branch elimination. Here, complexity mitigation is done both in terms of branch elimination and iteration reduction with negligible performance degradation. By reducing the computational complexity, decoding delay, power consumptions and error accumulation imparted by additional iterations etc can be minimized.