We introduce Meta-AdaM, a meta-learned adaptive optimizer with momentum, designed for few-shot learning tasks that pose significant challenges to deep learning models due to the limited number of labeled examples. Meta-learning has been successfully employed to address these challenges by transferring meta-learned prior knowledge to new tasks. Most existing works focus on meta-learning an optimal model initialization or an adaptive learning rate learner for rapid convergence. However, these approaches either neglect to consider weight-update history for the adaptive learning rate learner or fail to effectively integrate momentum for fast convergence, as seen in many-shot learning settings. To tackle these limitations, we propose a meta-learned learning rate learner that utilizes weight-update history as input to predict more appropriate learning rates for rapid convergence. Furthermore, for the first time, our approach incorporates momentum into the optimization process of few-shot learning via a double look-ahead mechanism, enabling rapid convergence similar to many-shot settings. Extensive experimental results on benchmark datasets demonstrate the effectiveness of the proposed Meta-AdaM.