Recent advances in algorithm-hardware co-design for deep neural networks (DNNs) have demonstrated their potential in automatically designing neural architectures and hardware designs. Nevertheless, it is still a challenging optimization problem due to the expensive training cost and the time-consuming hardware implementation, which makes the exploration on the vast design space of neural architecture and hardware design intractable. In this paper, we demonstrate that our proposed approach is capable of locating designs on the Pareto frontier. This capability is enabled by a novel three-phase co-design framework, with the following new features: (a) decoupling DNN training from the design space exploration of hardware architecture and neural architecture, (b) providing a hardware-friendly neural architecture space by considering hardware characteristics in constructing the search cells, (c) adopting Gaussian process to predict accuracy, latency and power consumption to avoid time-consuming synthesis and place-and-route processes. In comparison with the manually-designed ResNet101, InceptionV2 and MobileNetV2, we can achieve up to 5% higher accuracy with up to