Syntactic Transformer language models aim to achieve better generalization through simultaneously modeling syntax trees and sentences. While prior work has been focusing on adding constituency-based structures to Transformers, we introduce Dependency Transformer Grammars (DTGs), a new class of Transformer language model with explicit dependency-based inductive bias. DTGs simulate dependency transition systems with constrained attention patterns by modifying attention masks, incorporate the stack information through relative positional encoding, and augment dependency arc representation with a combination of token embeddings and operation embeddings. When trained on a dataset of sentences annotated with dependency trees, DTGs achieve better generalization while maintaining comparable perplexity with Transformer language model baselines. DTGs also outperform recent constituency-based models, showing that dependency can better guide Transformer language models. Our code is released at https://github.com/zhaoyd1/Dep_Transformer_Grammars.