First-order meta-learning algorithms have been widely used in practice to learn initial model parameters that can be quickly adapted to new tasks due to their efficiency and effectiveness. However, existing studies find that meta-learner can overfit to some specific adaptation when we have heterogeneous tasks, leading to significantly degraded performance. In Natural Language Processing (NLP) applications, datasets are often diverse and each task has its unique characteristics. Therefore, to address the overfitting issue when applying first-order meta-learning to NLP applications, we propose to reduce the variance of the gradient estimator used in task adaptation. To this end, we develop a variance-reduced first-order meta-learning algorithm. The core of our algorithm is to introduce a novel variance reduction term to the gradient estimation when performing the task adaptation. Experiments on two NLP applications: few-shot text classification and multi-domain dialog state tracking demonstrate the superior performance of our proposed method.