Deep learning-based code processing models have shown good performance for tasks such as predicting method names, summarizing programs, and comment generation. However, despite the tremendous progress, deep learning models are often prone to adversarial attacks, which can significantly threaten the robustness and generalizability of these models by leading them to misclassification with unexpected inputs. To address the above issue, many deep learning testing approaches have been proposed, however, these approaches mainly focus on testing deep learning applications in the domains of image, audio, and text analysis, etc., which cannot be directly applied to neural models for code due to the unique properties of programs. In this paper, we propose a coverage-based fuzzing framework, CoCoFuzzing, for testing deep learning-based code processing models. In particular, we first propose ten mutation operators to automatically generate valid and semantically preserving source code examples as tests; then we propose a neuron coverage-based approach to guide the generation of tests. We investigate the performance of CoCoFuzzing on three state-of-the-art neural code models, i.e., NeuralCodeSum, CODE2SEQ, and CODE2VEC. Our experiment results demonstrate that CoCoFuzzing can generate valid and semantically preserving source code examples for testing the robustness and generalizability of these models and improve the neuron coverage. Moreover, these tests can be used to improve the performance of the target neural code models through adversarial retraining.