In this paper, we propose an improved version of the min-sum algorithm for low density parity check (LDPC) code decoding, which we call “adaptive normalized BP-based” algorithm. Our decoder provides a compromise solution between the belief propagation and the min-sum algorithms by adding an exponent offset to each variable node’s intrinsic information in the check node update equation. The extrinsic information from the min-sum decoder is then adjusted by applying a negative power of two scale factor, which can be easily implemented by right shifting the min-sum extrinsic information. The difference between our approach and other adaptive normalized min-sum decoders is that we select the normalization scale factor using a clear analytical approach based on underlying principles. Simulation results show that the proposed decoder outperforms the min-sum decoder and performs very close to the BP decoder, but with lower complexity.