Quantum one-way function (QOWF) was proposed for quantum cryptography, which was computable but almost irreversible in quantum polynomial time. Full quantum one-way function (F-QOWF) is one of the most important models of QOWF, which deals with quantum states. Although the universal construction of full quantum one-way function has been proposed, there is still little further discussion on the entangled input, specific function instantiation and application scenarios of F-QOWF. In this paper, we introduce quantum hypergraph states into the universal construction of F-QOWF. Quantum hypergraph states are highly entangled multi-party states constructed from the hypergraph. By applying quantum hypergraph states to the new F-QOWF, we generalize the universal construction of F-QOWF to entangled states. The application to quantum aggregate signature shows that quantum hypergraph states help the new F-QOWF be well applied to quantum multi-party cryptographic protocols.