Aspect-based sentiment classification aims to identify sentiment polarity expressed towards a given opinion target in a sentence. The sentiment polarity of the target is not only highly determined by sentiment semantic context but also correlated with the concerned opinion target. Existing works cannot effectively capture and store the inter-dependence between the opinion target and its context. To solve this issue, we propose a novel model of Attentive Neural Turing Machines (ANTM). Via interactive read-write operations between an external memory storage and a recurrent controller, ANTM can learn the dependable correlation of the opinion target to context and concentrate on crucial sentiment information. Specifically, ANTM separates the information of storage and computation, which extends the capabilities of the controller to learn and store sequential features. The read and write operations enable ANTM to adaptively keep track of the interactive attention history between memory content and controller state. Moreover, we append target entity embeddings into both input and output of the controller in order to augment the integration of target information. We evaluate our model on SemEval2014 dataset which contains reviews of Laptop and Restaurant domains and Twitter review dataset. Experimental results verify that our model achieves state-of-the-art performance on aspect-based sentiment classification.