The goal of molecular optimization (MO) is to discover molecules that acquire improved pharmaceutical properties over a known starting molecule. Despite many recent successes of new approaches for MO, these methods were typically developed for particular properties with rich annotated training examples. Thus, these approaches are difficult to implement in real scenes where only a small amount of pharmaceutical data is usually available due to the expense and significant effort required for the data collection. Here, we propose a new approach, Meta-MO, for molecular optimization with a handful of training samples based on the well-recognized first-order meta-learning algorithms. By using a set of meta tasks with rich training samples, Meta-MO trains a meta model through the meta-learning optimization and adapts the learned model to new low-resource MO tasks. Meta-MO was shown to consistently outperform several pretraining and multitask training procedures, providing an average improvement in the success rate of 4.3% on a large-scale bioactivity data set with diverse target variations. We also observed that Meta-MO resulted in the best performing models across fine-tuning sets with only dozens of samples. To the best of our knowledge, this is the first study to apply meta learning to MO tasks. More importantly, such a strategy could be further extended to many low-resource scenarios in real-world drug design.