To facilitate efficient embedded and hardware implementations of deep neural networks (DNNs), a number of prior work are dedicated to model compression techniques. The target is to simultaneously reduce the model storage size and accelerate the computation, with minor effect on accuracy. Two important categories of DNN model compression techniques are weight pruning and weight quantization. The former leverages the redundancy in the number of weights, whereas the latter leverages the redundancy in bit representation of weights. These two sources of redundancy can be combined, thereby leading to a higher degree of DNN model compression. However, there lacks a systematic framework of joint weight pruning and quantization of DNNs, thereby limiting the available model compression ratio. Moreover, the computation reduction, energy efficiency improvement, and hardware performance overhead need to be accounted for besides simply model size reduction.To address these limitations, we present ADMM-NN, the first algorithm-hardware co-optimization framework of DNNs using Alternating Direction Method of Multipliers (ADMM), a powerful technique to deal with non-convex optimization problems with possibly combinatorial constraints. The first part of ADMM-NN is a systematic, joint framework of DNN weight pruning and quantization using ADMM. It can be understood as a smart regularization technique with regularization target dynamically updated in each ADMM iteration, thereby resulting in higher performance in model compression than prior work. The second part is hardware-aware DNN optimizations to facilitate hardware-level implementations. We perform ADMM-based weight pruning and quantization accounting for (i) the computation reduction and energy efficiency improvement, and (ii) the hardware performance overhead due to irregular sparsity. The first requirement prioritizes the convolutional layer compression over fully-connected layers, while the latter requires a concept of the break-even pruning ratio, defined as the minimum pruning ratio of a specific layer that results in no hardware performance degradation.Without accuracy loss, we can achieve 85× and 24× pruning on LeNet-5 and AlexNet models, respectively, significantly higher than prior work. The improvement becomes more significant when focusing on computation reductions. Combining weight pruning and quantization, we achieve 1,910× and 231× reductions in overall model size on these two benchmarks, when focusing on data storage. Highly promising results are also observed on other representative to appear in ASPLOS 2019 DNNs such as VGGNet and ResNet-50. We release codes and models at anonymous link http://bit.ly/2M0V7DO.