Deep learning-based autoencoder has shown considerable potential in channel state information (CSI) feedback. However, the excellent feedback performance achieved by autoencoder is at the expense of a high computational complexity. In this paper, a knowledge distillation-based neural network lightweight strategy is introduced to deep learning-based CSI feedback to reduce the computational requirement. The key idea is to transfer the dark knowledge learned by a complicated teacher network to a lightweight student network, thereby improving the performance of the student network. First, an autoencoder distillation method is proposed by forcing the student autoencoder to mimic the output of the teacher autoencoder. Then, given the more limited computational power at the user equipment, an encoder distillation method is proposed where distillation is only performed to student encoder at the user equipment and the teacher decoder is directly used at the base stataion. The numerical simulation results show that the performance of student autoencoder can be considerably improved after knowledge distillation and encoder distillation can further improve the feedback performance and reduce the complexity.