Memristor-based crossbars, which can achieve 1-2 orders of magnitude energy efficiency improvement, have been introduced to accelerate neural networks of machine learning tasks. Due to the high voltage pulses repeatedly applied onto memristors during programming and online tuning, the effective resistance ranges of the memristors actually decreases as a result of aging, which eventually impairs the inference accuracy of the neural network executed on the memristor-based crossbar. In this paper, we propose a co-design framework combining aging aware retraining and gradient sparsification to mitigate the impact of aging and extend the lifetime of the crossbar. Experimental results show that the proposed methods can effectively increase the inference accuracy by up to 16% when with severe aging, while the crossbar lifetime can be extended by up to 2.7X.