This paper proposes an improved Logarithmic Maximum A Posteriori (Log-MAP) algorithm for Turbo decoding in the Third Generation Partnership Project Long Term Evolution (3GPP LTE). In the proposed algorithm, we exploit the understanding of polynomial regression function to approximately compute the logarithm term (also called correction function) in the Jacobian logarithmic function. The goal is to replace the correction function on an other function with the approximated performance and the reduced computational complexity. Simulation results show that the performance of the proposed algorithm is closest to the Log-MAP algorithm for Turbo decoding under Additive White Gaussian Noise (AWGN) channel and can offer about maximum 0.4dB performance gain than the Max-Log-MAP algorithm and higher than other Log-MAP-based algorithms. The proposed algorithm has much simpler computational complexity in comparison with the Log-MAP algorithm and slightly increased compared to the Max-Log-MAP algorithm