Executing computer programs described in natural language has long been a pursuit of computer science. With the advent of enhanced natural language understanding capabilities exhibited by large language models (LLMs), the path toward this goal has been illuminated. In this paper, we seek to examine the capacity of present-day LLMs to comprehend and execute algorithms outlined in natural language. We established an algorithm test set sourced from Introduction to Algorithm, a well-known textbook that contains many representative widely-used algorithms. To systematically assess LLMs’ code execution abilities, we selected 30 algorithms, generated 300 random-sampled instances in total, and evaluated whether popular LLMs can understand and execute these algorithms. Our findings reveal that LLMs, notably GPT-4, can effectively execute programs described in natural language, as long as no heavy numeric computation is involved. We believe our findings contribute to evaluating LLMs’ code execution abilities and would encourage further investigation and application for the computation power of LLMs.