Large Language Models have achieved impressive performance across various natural language generation tasks. However, their lack of a reliable control mechanism limits their effectiveness in applications that require strict adherence to predefined taxonomies, syntactic structures, or domain-specific rules. Existing approaches, such as fine-tuning and prompting, remain insufficient to ensure compliance with these requirements, particularly in low-resource scenarios and structured text generation tasks.To address these limitations, we introduce GRAMMAR-LLM, a novel framework that integrates formal grammatical constraints into the LLM decoding process. GRAMMAR-LLM enforces syntactic correctness in linear time while maintaining expressiveness in grammar rule definition. To achieve this, we define a class of grammars, called LL(prefix), – which we show to be equivalent to LL(1) – specifically designed for their use with LLMs. These grammars are expressive enough to support common tasks such as hierarchical classification, vocabulary restriction, and structured parsing. We formally prove that LL(prefix) grammars can be transformed into LL(1) grammars in linear time, ensuring efficient processing via deterministic pushdown automata. We evaluate GRAMMAR-LLM across diverse NLP tasks, including hierarchical classification, sign language translation, and semantic parsing. Our experiments, conducted on models such as LLaMA 3 (for classification and translation) and AMRBART (for parsing), demonstrate that GRAMMAR-LLM consistently improves task performance across zero-shot, few-shot, and fine-tuned settings.