Speech enhancement aims to reduce the noise and improve the quality and intelligibility of noisy speech. Long short-term memory (LSTM) network frameworks have achieved great success on many speech enhancement applications. In this paper, the ordered neurons long short-term memory (ON-LSTM) network with a new inductive bias to differential the long/short-term information in each neuron is proposed for speech enhancement. Comparing the low-ranking neurons with short-term or local information, the high-ranking neurons which contain the long-term or global information always update less frequently for a wide range of influence. Thus, the ON-LSTM can automatically learn the clean speech information from noisy input and show better expressive ability. We also propose a rearrangement concatenation rule to connect the ON-LSTM outputs of forward and backward layers to construct the bidirectional ON-LSTM (Bi-ONLSTM) for further performance improvement. The experimental results reveal that the proposed ON-LSTM schemes produce better enhancement performance than the vanilla LSTM baseline. And visualization result shows that our proposed model can effectively capture clean speech components from noisy inputs.