With the growing attention on learning-to-learn new tasks using only a few examples, meta-learning has been widely used in numerous problems such as few-shot classification, reinforcement learning, and domain generalization. However, meta-learning models are prone to overfitting when there are no sufficient training tasks for the meta-learners to generalize. Although existing approaches such as Dropout are widely used to address the overfitting problem, these methods are typically designed for regularizing models of a single task in supervised training. In this paper, we introduce a simple yet effective method to alleviate the risk of overfitting for gradient-based meta-learning. Specifically, during the gradient-based adaptation stage, we randomly drop the gradient in the inner-loop optimization of each parameter in deep neural networks, such that the augmented gradients improve generalization to new tasks. We present a general form of the proposed gradient dropout regularization and show that this term can be sampled from either the Bernoulli or Gaussian distribution. To validate the proposed method, we conduct extensive experiments and analysis on numerous computer vision tasks, demonstrating that the gradient dropout regularization mitigates the overfitting problem and improves the performance upon various gradient-based meta-learning frameworks.