Nowadays, we are witnessing an increasing demand in both corporates and academia for exploiting Deep Learning (DL) to solve complex real-world problems. A DL program encodes the network structure of a desirable DL model and the process by which the model learns from the training dataset. Like any software, a DL program can be faulty, which implies substantial challenges of software quality assurance, especially in safety-critical domains. It is therefore crucial to equip DL development teams with efficient fault detection techniques and tools. In this article, we propose NeuraLint, a model-based fault detection approach for DL programs, using meta-modeling and graph transformations. First, we design a meta-model for DL programs that includes their base skeleton and fundamental properties. Then, we construct a graph-based verification process that covers 23 rules defined on top of the meta-model and implemented as graph transformations to detect faults and design inefficiencies in the generated models (i.e., instances of the meta-model). First, the proposed approach is evaluated by finding faults and design inefficiencies in 28 synthesized examples built from common problems reported in the literature. Then NeuraLint successfully finds 64 faults and design inefficiencies in 34 real-world DL programs extracted from Stack Overflow posts and GitHub repositories. The results show that NeuraLint effectively detects faults and design issues in both synthesized and real-world examples with a recall of 70.5% and a precision of 100%. Although the proposed meta-model is designed for feedforward neural networks, it can be extended to support other neural network architectures such as recurrent neural networks. Researchers can also expand our set of verification rules to cover more types of issues in DL programs.