With the great success of deep learning (DL) in image classification, speech recognition, and other fields, more and more studies have applied various neural networks (NNs) to wireless resource allocation. Generally speaking, these artificial intelligent (AI) models are trained under some special learning hypotheses, especially that the statistics of the training data are static during the training stage. However, the distribution of channel state information (CSI) is constantly changing in the real-world wireless communication environment. Therefore, it is essential to study effective dynamic DL technologies to solve wireless resource allocation problems. In this paper, we propose a novel framework, named meta-gating, for solving resource allocation problems in an episodically dynamic wireless environment, where the CSI distribution changes over periods and remains constant within each period. The proposed framework, consisting of an inner network and an outer network, aims to adapt to the dynamic wireless environment by achieving three important goals, i.e., seamlessness, quickness and continuity. Specifically, for the former two goals, we propose a training method by combining a model-agnostic meta-learning (MAML) algorithm with an unsupervised learning mechanism. With this training method, the inner network is able to fast adapt to different channel distributions because of the good initialization. As for the goal of continuity, the outer network can learn to evaluate the importance of inner network's parameters under different CSI distributions, and then decide which subset of the inner network should be activated through the gating operation. Additionally, we theoretically analyze the performance of the proposed meta-gating framework.