Magnetic interactions in combination with nontrivial band structures can give rise to several exotic physical properties such as a large anomalous Hall effect, the anomalous Nernst effect, and the topological Hall effect (THE). Antiferromagnetic (AFM) materials exhibit the THE due to the presence of nontrivial spin structures. EuCuAs crystallizes in a hexagonal structure with an AFM ground state (Néel temperature ∼ 16 K). In this work, we observe a large topological Hall resistivity of ∼7.4 μΩ-cm at 13 K which is significantly higher than the giant topological Hall effect of Gd2PdSi3 (∼3 μΩ-cm). Neutron diffraction experiments reveal that the spins form a transverse conical structure during the metamagnetic transition, resulting in the large THE. In addition, by controlling the magnetic ordering structure of EuCuAs with an external magnetic field, several fascinating topological states such as Dirac and Weyl semimetals have been revealed. These results suggest the possibility of spintronic devices based on antiferromagnets with tailored noncoplanar spin configurations.