The formation of a functional spindle requires microtubule (MT) nucleation from within the spindle, which depends on augmin. How augmin contributes to MT formation and organization is not known because augmin-dependent MTs have never been specifically visualized. In this paper, we identify augmin-dependent MTs and their connections to other MTs by electron tomography and 3D modeling. In metaphase spindles of human cells, the minus ends of MTs were located both around the centriole and in the body of the spindle. When augmin was knocked down, the latter population of MTs was significantly reduced. In control cells, we identified connections between the wall of one MT and the minus end of a neighboring MT. Interestingly, the connected MTs were nearly parallel, unlike other examples of end-wall connections between cytoskeletal polymers. Our observations support the concept of augmin-dependent MT nucleation at the walls of existing spindle MTs. Furthermore, they suggest a mechanism for maintaining polarized MT organization, even when noncentrosomal MT initiation is widespread.