Large language models have demonstrated exceptional language understanding capabilities in many NLP tasks. Sparsely activated mixture-of-experts (MoE) has emerged as a promising solution for scaling models while maintaining a constant number of computational operations. Existing MoE models adopt a fixed gating network where each token is computed by the same number of experts. This contradicts our intuition that the tokens in each sequence vary in terms of their linguistic complexity and, consequently, require different computational costs. Little is discussed in prior research on the trade-off between computation per token and model performance. This paper introduces adaptive gating in MoE, a flexible training strategy that allows tokens to be processed by a variable number of experts based on expert probability distribution. Adaptive gating preserves sparsity while improving training efficiency. We further draw upon curriculum learning to better align the order of training samples and maximize the training time savings. Extensive experiments on diverse NLP tasks show that adaptive gating reduces at most 22.5% training time while maintaining inference quality. Moreover, we conduct a comprehensive analysis of the gating decisions and present our insights on which tokens are inherently difficult to process, depending on the specific language task.