On-device Deep Neural Network (DNN)  inference consumes significant computing resources and development efforts. To alleviate that, we propose LUT-NN, the first system to empower inference by table lookup, to reduce inference cost. LUT-NN learns the typical features for each operator, named centroid, and precompute the results for these centroids to save in lookup tables. During inference, the results of the closest centroids with the inputs can be read directly from the table, as the approximated outputs without computations. LUT-NN integrates two major novel techniques: (1)  differentiable centroid learning through backpropagation, which adapts three levels of approximation to minimize the accuracy impact by centroids; (2)  table lookup inference execution, which comprehensively considers different levels of parallelism, memory access reduction, and dedicated hardware units for optimal performance. LUT-NN is evaluated on multiple real tasks, covering image and speech recognition, and nature language processing. Compared to related work, LUT-NN improves accuracy by 66% to 92%, achieving similar level with the original models. LUT-NN reduces the cost at all dimensions, including FLOPs () , model size () , latency () , memory () , and power () .