Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks (NNs), e.g., an approximator and a predictor. The approximator provides the approximate results, while the predictor predicts whether the input data is safe to approximate with the given quality requirement. However, it is non-trivial and time-consuming to make these two neural network coordinate---they have different optimization objectives---by training them separately. This paper proposes a novel neural network structure---AXNet---to fuse two NNs to a holistic end-to-end trainable NN. Leveraging the philosophy of multi-task learning, AXNet can tremendously improve the invocation (proportion of safe-to-approximate samples) and reduce the approximation error. The training effort also decrease significantly. Experiment results show 50.7% more invocation and substantial cuts of training time when compared to existing neural network based approximate computing framework.