Neural networks trained by backpropagation have achieved tremendous successes on numerous intelligent tasks. However, naïve gradient-based training and updating methods on memristors impede applications due to intrinsic material properties. Here, we built a 39 nm 1 Gb phase change memory (PCM) memristor array and quantified the unique resistance drift effect. On this basis, spontaneous sparse learning (SSL) scheme that leverages the resistance drift to improve PCM-based memristor network training is developed. During training, SSL regards the drift effect as spontaneous consistency-based distillation process that reinforces the array weights at the high-resistance state continuously unless the gradient-based method switches them to low resistance. Experiments show that the SSL not only helps the convergence of network with better performance and sparsity controllability without additional computation in handwritten digit classification. This work promotes the learning algorithms with the intrinsic properties of memristor devices, opening a new direction for development of neuromorphic computing chips.