Aiming at the problems of incomplete semantic representation of hyper-relational facts as well as insufficient task accuracy and generalization ability caused by the qualifier sparsity in Hyper-relational Knowledge Graphs （HKGs）， a Large language model-driven method for Qualifier Enhancement in HKGs （L-EQs） was proposed. First， semantically rich description information was obtained from the associated knowledge bases to mitigate semantic ambiguity caused by the same labels of entities and relations. Second， prompt templates were used to guide the LLM in generating the matched qualifiers and their semantic explanations as external knowledge. To ensure the quality of the qualifiers， an iterative prompting strategy was employed to filter the generated qualifiers， with multiple iterations conducted until the predetermined quantity was reached. Third， embeddings of external knowledge were constructed through the semantic explanations， and an external knowledge aggregation module was introduced to suppress noise， thereby providing high-quality semantic support for the downstream task by integrating external knowledge and original knowledge embeddings. Finally， the task results were predicted through a decoder， and extensive experiments were conducted on the open-source datasets WikiPeople and WD50K to validate the effectiveness of the L-EQs. Experimental results show that compared to the optimal results of the baseline models， the Mean Reciprocal Rank （MRR）， Hit@1， Hit@5， and Hit@10 of the L-EQs are increased by 8.4， 4.7， 5.3， and 6.8 percentage points， respectively， on the WikiPeople dataset， and are improved by 4.8， 2.3， 2.7， and 3.0 percentage points， respectively， on the WD50K. L-EQs addresses the qualifier sparsity in HKG and the issues caused by the incomplete semantic representations.