The utilization of personal sensitive data in training face recognition (FR) models poses significant privacy concerns, as adversaries can employ model inversion attacks (MIA) to infer the original training data. Existing defense methods, such as data augmentation and differential privacy, have been employed to mitigate this issue. However, these methods often fail to strike an optimal balance between privacy and accuracy. To address this limitation, this paper introduces an adaptive hybrid masking algorithm against MIA. Specifically, face images are masked in the frequency domain using an adaptive MixUp strategy. Unlike the traditional MixUp algorithm, which is predominantly used for data augmentation, our modified approach incorporates frequency domain mixing. Previous studies have shown that increasing the number of images mixed in MixUp can enhance privacy preservation but at the expense of reduced face recognition accuracy. To overcome this trade-off, we develop an enhanced adaptive MixUp strategy based on reinforcement learning, which enables us to mix a larger number of images while maintaining satisfactory recognition accuracy. To optimize privacy protection, we propose maximizing the reward function (i.e., the loss function of the FR system) during the training of the strategy network. While the loss function of the FR network is minimized in the phase of training the FR network. The strategy network and the face recognition network can be viewed as antagonistic entities in the training process, ultimately reaching a more balanced trade-off. Experimental results demonstrate that our proposed hybrid masking scheme outperforms existing defense algorithms in terms of privacy preservation and recognition accuracy against MIA.