Testing is an essential part of modern software engineering to build reliable programs. As testing the software is important but expensive, automatic test case generation methods have become popular in software development. Unlike traditional search-based coverage-guided test generation like fuzzing, neural test generation backed by large language models can write tests that are semantically meaningful and can be understood by other maintainers. However, compared to regular code corpus, unit tests in the datasets are limited in amount and diversity. In this paper, we present a novel data augmentation technique **FuzzAug**, that combines the advantages of fuzzing and large language models. FuzzAug not only keeps valid program semantics in the augmented data, but also provides more diverse inputs to the function under test, helping the model to associate correct inputs embedded with the function's dynamic behaviors with the function under test. We evaluate FuzzAug's benefits by using it on a neural test generation dataset to train state-of-the-art code generation models. By augmenting the training set, our model generates test cases with $11\%$ accuracy increases. Models trained with FuzzAug generate unit test functions with double the branch coverage compared to those without it. FuzzAug can be used across various datasets to train advanced code generation models, enhancing their utility in automated software testing. Our work shows the benefits of using dynamic analysis results to enhance neural test generation. Code and data will be publicly available.