A three-dimensional (3D) isogeometric/discrete-element coupling method is presented for modeling contact/impact between structures and particles. This method takes advantages of the geometry smoothness and exactness of isogeometric analysis (IGA) for continuous solid media and the effectiveness and flexibility of the discrete element method (DEM) for particulate matters. The coupling procedure for handling interactions between IGA elements and discrete elements (DEs) includes global search, local search and interaction calculation. In the global search, the CGRID method is modified to detect potential contact pairs between IGA elements and DEs based on their bounding box representations. The strong convex hull property of a NURBS control mesh plays an important part in the bounding box representation of IGA elements. In the local search, the proposed approach treats each spherical DE centroid as a slave node and the contact surface of each IGA element as the master surface. The projection of a DE centroid onto an IGA element contact surface is solved by modifying the simplex method and Brent iterations. The contact force between an IGA element and a DE is determined from their penetration by using a (nonlinear) penalty function based method. The whole coupled system is solved by the explicit time integration within a updated Lagrangian scheme. Finally, three impact examples, including the impact of two symmetric bars, a tube onto a footing strip, and an assembly of granular particles to a tailor rolled blank, are simulated in elastic regime to assess the accuracy and applicability of the proposed method.