This paper proposes an adaptive normalized min-sum algorithm for the decoding of low-density parity check (LDPC) codes, which utilizes an adaptive normalization factor to improve the accuracy of the soft information transferred during the iterative decoding process, and provides superior performance accordingly. This adaptive normalization factor can be adjusted dynamically and adaptively at each decoding iteration according to a look-up table obtained via training and simulation. Its implementation facility and independence from the channel characteristics make the proposed adaptive normalized min-sum algorithm expect a wide application. Simulation results show that the proposed algorithm can achieve performance much closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for DVB-S2's rate 2/5 and 3/5 LDPC codes over the additive white Gaussian noise (AWGN) channel.