In Text-to-SQL generation, large language models (LLMs) have shown strong generalization and adaptability. However, LLMs sometimes generate hallucinations, i.e.,unrealistic or illogical content, which leads to incorrect SQL queries and negatively impacts downstream applications. Detecting these hallucinations is particularly challenging. Existing Text-to-SQL error detection methods, which are tailored for traditional deep learning models, face significant limitations when applied to LLMs. This is primarily due to the scarcity of ground-truth data. To address this challenge, we propose SQLHD, a novel hallucination detection method based on metamorphic testing (MT) that does not require standard answers. SQLHD splits the detection task into two sequentiial stages: schema-linking hallucination detection via eight structure-aware Metamorphic Relations (MRs) that perturb comparative words, entities, sentence structure or database schema, and logical-synthesis hallucination detection via nine logic-aware MRs that mutate prefix words, extremum expressions, comparison ranges or the entire database. In each stage the LLM is invoked separately to generate schema mappings or SQL artefacts; the follow-up outputs are cross-checked against their source counterparts through the corresponding MRs, and any violation is flagged as a hallucination without requiring ground-truth SQL. The experimental results demonstrate our method's superior performance in terms of the F1-score, which ranges from 69.36\% to 82.76\%. Additionally, SQLHD demonstrates superior performance over LLM Self-Evaluation methods, effectively identifying hallucinations in Text-to-SQL tasks.