Artificial neural networks are powerful models, which have been widely applied into many aspects of machine translation, such as language modeling and translation modeling. Though notable improvements have been made in these areas, the reordering problem still remains a challenge in statistical machine translations. In this paper, we present a novel neural reordering model that directly models word pairs and alignment. By utilizing LSTM recurrent neural networks, much longer context could be learned for reordering prediction. Experimental results on NIST OpenMT12 Arabic-English and Chinese-English 1000-best rescoring task show that our LSTM neural reordering feature is robust and achieves significant improvements over various baseline systems.