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In the decoding process of LDPC codes, variable node messages often fluctuate continuously and thereby become the hindrance to the successful decoding. This paper proposes an adaptive erasure belief propagation (AE-BP) decoding algorithm to reduce the influence of these unreliable messages. The idea behind AE-BP is recording the continuous fluctuant times of variable nodes by introducing a sequence of counters, and then adaptively erasing the messages according to their fluctuant times so that other messages would recover to more precise states. Semi-Gaussian approximation demonstrates adaptive erasure is a good candidate towards offsetting the defect of unreliable messages. Experimental simulations show that, for LDPC codes AE-BP outperforms most decoding algorithms in the literature.