With the growing importance of error correction in different communication systems, using an efficient and easily implementable code is always appreciated. One of the most important codes is the low-density parity-check (LDPC) code. Two main iterative decoding algorithms are usually used, namely the sum-product (SP) algorithm (also referred to as belief propagation) and the min-sum (MS). The SP algorithm is more accurate but suffers from very high complexity. On the other hand, the MS algorithm has a much lower complexity at the expense of some performance degradation. To handle this performance degradation, many algorithms were presented in the literature as improvements for the MS, like the scaled MS and the offset MS. However, all those improved algorithms are more complex than the traditional MS. In this study, an efficient and low complexity LDPC decoding algorithm, called selective max-min (SMM), is proposed. The SMM performance is closer to SP than to MS as long as the average number of ones per column in the parity check matrix is around or less than 4 (which is the case for most of the communication systems using LDPC). On the other hand, the SMM exhibits only a minor complexity increase over traditional MS making it suitable for practical implementation.