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Deep neural networks (DNNs) come with many forms, such as convolutional neural networks, multilayer perceptron and recurrent neural networks, to meet diverse needs of machine learning applications. However, existing DNN accelerator designs, when used to execute multiple neural networks, suffer from underutilization of processing elements, heavy feature map traffic, and large area overhead. In this paper, we propose a novel approach, Polymorphic Accelerators, to address the flexibility issue fundamentally. We introduce the abstraction of logical accelerators to decouple the fixed mapping with physical resources. Three procedures are proposed that work collaboratively to reconfigure the accelerator for the current network that is being executed and to enable cross-layer data reuse among logical accelerators. Evaluation results show that the proposed approach achieves significant improvement in data reuse, inference latency and performance, e.g., 1.52x and 1.63x increase in throughput compared with state-of-the-art flexible dataflow approach and resource partitioning approach, respectively. This demonstrates the effectiveness and promise of polymorphic accelerator architecture.