Compute-efficient training of large language models (LLMs) has become an important research problem. In this work, we consider data pruning as a method of data-efficient training of LLMs, where we take a data compression view on data pruning. We argue that the amount of information of a sample, or the achievable compression on its description length, represents its sample importance. The key idea is that, less informative samples are likely to contain redundant information, and thus should be pruned first. We leverage log-likelihood function of trained models as a surrogate to measure information content of samples. Experiments reveal a surprising insight that information-based pruning can enhance the generalization capability of the model, improves upon language modeling and downstream tasks as compared to the model trained on the entire dataset.