Black-box Large Language Models (LLMs) have shown great power in solving various tasks and are considered general problem solvers. However, LLMs still fail in many specific tasks although understand the task instruction. In this paper, we focus on the problem of boosting the ability of black-box LLMs to solve downstream tasks. We propose ExpNote, an automated framework to help LLMs better adapt to unfamiliar tasks through reflecting and noting experiences from training data and retrieving them from external memory during testing. We evaluate ExpNote on multiple tasks and the experimental results demonstrate that the proposed method significantly improves the performance of black-box LLMs. The data and code are available at https://github.com/forangel2014/ExpNote.