Modeling fiber-reinforced concrete within the framework of the finite element method presents a significant hurdle due to the slenderness of the fiber, which, if largely skewed elements are to be avoided, necessitates the use of very fine meshes for fiber discretization, as well as for concrete matrix discretization in the vicinity of the fibers. The use of fine meshes leads to significant computational effort in three-dimensional simulation setups. This contribution presents an approach for a more efficient simulation of fiber-reinforced concrete in 3D, in which rather than explicitly meshing the fiber geometry in 3D, the fibers are discretized with 1D line elements and coupled with the 3D bulk material using a newly implemented connection element. The coupling of the 1D fibers with the 3D concrete matrix is done by imposing constraints on the displacement fields of the fiber and the concrete materials at the fiber-concrete interface. The interface response description is governed by distinct constitutive laws with respect to fiber orientation. In the direction perpendicular to the fiber, relative displacements are constrained to near-zero values by means of the penalty method. Tangentially to the fiber orientation, the interface behavior is governed by means of a piecewise-linear traction separation law to allow for a fiber slip in the tangential direction. To facilitate larger-scale testing of the connection element, a custom algorithm has been developed for mesh creation, which enables the generation of meshes with diverse fiber disctributions. The connection element shows promising results for efficiently simulating fiber-reinforced concrete with consideration for the micro-mechanical behavior of the fiber-concrete interface.