Face recognition (FR) models can be easily fooled by adversarial examples, which are crafted by adding imperceptible perturbations on benign face images. To improve the transferability of adversarial examples on FR models, we propose a novel attack method called Beneficial Perturbation Feature Augmentation Attack (BPFA), which reduces the overfitting of the adversarial examples to surrogate FR models by the adversarial strategy. Specifically, in the backpropagation step, BPFA records the gradients on pre-selected features and uses the gradient on the input image to craft adversarial perturbation to be added on the input image. In the next forward propagation step, BPFA leverages the recorded gradients to add perturbations(i.e., beneficial perturbations) that can be pitted against the adversarial perturbation added on the input image on their corresponding features. The above two steps are repeated until the last backpropagation step before the maximum number of iterations is reached. The optimization process of the adversarial perturbation added on the input image and the optimization process of the beneficial perturbations added on the features correspond to a minimax two-player game. Extensive experiments demonstrate that BPFA outperforms the state-of-the-art gradient-based adversarial attacks on FR.