In the academic field, the research on human motion prediction tasks mainly focuses on exploiting the observed information to forecast human movements accurately in the near future horizon. However, a significant gap appears when it comes to the application field, as current models are all trained offline, with fixed parameters that are inherently suboptimal to handle the complex yet ever-changing nature of human behaviors. To bridge this gap, in this paper, we introduce the task of online meta adaptation for human motion prediction, based on the insight that finding "smart weights" capable of swift adjustments to suit different motion contexts along the time is a key to improving predictive accuracy. We propose MoML, which ingeniously borrows the bilevel optimization spirit of model-agnostic meta-learning, to transform previous predictive mistakes into strong inductive biases to guide online adaptation. This is achieved by our MoAdapter blocks that can learn error information by facilitating efficient adaptation via a few gradient steps, which fine-tunes our meta-learned "smart" initialization produced by the generic predictor. Considering real-time requirements in practice, we further propose Fast-MoML, a more efficient variant of MoML that features a closed-form solution instead of conventional gradient update. Experimental results show that our approach can effectively bring many existing offline motion prediction models online, and improves their predictive accuracy.