Deep neural networks (DNNs) are vulnerable to adversarial examples. And, the adversarial examples have transferability, which means that an adversarial example for a DNN model can fool another model with a non-trivial probability. This gave birth to the transfer-based attack where the adversarial examples generated by a surrogate model are used to conduct black-box attacks. There are some work on generating the adversarial examples from a given surrogate model with better transferability. However, training a special surrogate model to generate adversarial examples with better transferability is relatively under-explored. This paper proposes a method for training a surrogate model with dark knowledge to boost the transferability of the adversarial examples generated by the surrogate model. This trained surrogate model is named dark surrogate model (DSM). The proposed method for training a DSM consists of two key components: a teacher model extracting dark knowledge, and the mixing augmentation skill enhancing dark knowledge of training data. We conducted extensive experiments to show that the proposed method can substantially improve the adversarial transferability of surrogate models across different architectures of surrogate models and optimizers for generating adversarial examples, and it can be applied to other scenarios of transfer-based attack that contain dark knowledge, like face verification. Our code is publicly available at \url{https://github.com/ydc123/Dark_Surrogate_Model}.