Hypergraph states are generalizations of graph states where controlled-Z gates on edges are replaced with generalized controlled-Z gates on hyperedges. Hypergraph states have several advantages over graph states. For example, certain hypergraph states, such as the Union Jack states, are universal resource states for measurement-based quantum computing with only Pauli measurements, while graph state measurement-based quantum computing needs non-Clifford basismeasurements. Furthermore, it is impossible to classically efficiently sample measurement results on hypergraph states unless the polynomial hierarchy collapses to the third level. Although several protocols have been proposed to verify graph states with only sequential single-qubit Pauli measurements, there was no verification method for hypergraph states. In this paper, we propose a method for verifying a certain class of hypergraph states with only sequential single-qubit Pauli measurements. Importantly, no i.i.d. property of samples is assumed in our protocol: any artificial entanglement among samples cannot fool the verifier. As applications of our protocol, we consider verified blind quantum computing with hypergraph states, and quantum computational supremacy demonstrations with hypergraph states.