Pre-trained language models have achieved remarkable successes in natural language processing tasks, coming at the cost of increasing model size. To address this issue, knowledge distillation (KD) has been widely applied to compress language models. However, typical KD approaches for language models have overlooked the difficulty of training examples, suffering from incorrect teacher prediction transfer and sub-efficient training. In this paper, we propose a novel KD framework, Tutor-KD, which improves the distillation effectiveness by controlling the difficulty of training examples during pre-training. We introduce a tutor network that generates samples that are easy for the teacher but difficult for the student, with training on a carefully designed policy gradient method. Experimental results show that Tutor-KD significantly and consistently outperforms the state-of-the-art KD methods with variously sized student models on the GLUE benchmark, demonstrating that the tutor can effectively generate training examples for the student.