The intrinsic error tolerance of neural network (NN) makes approximate computing a promising technique to improve the energy efficiency of NN inference. Conventional approximate computing focuses on balancing the efficiency-accuracy trade-off for existing pre-trained networks, which can lead to suboptimal solutions. In this paper, we propose AxTrain, a hardware-oriented training framework to facilitate approximate computing for NN inference. Specifically, AxTrain leverages the synergy between two orthogonal methods---one actively searches for a network parameters distribution with high error tolerance, and the other passively learns resilient weights by numerically incorporating the noise distributions of the approximate hardware in the forward pass during the training phase. Experimental results from various datasets with near-threshold computing and approximation multiplication strategies demonstrate AxTrains ability to obtain resilient neural network parameters and system energy efficiency improvement.