We compute the next-to-maximally-helicity-violating one-loop n-gluon amplitudes in N=1 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and constitute the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. They can be considered as important contributions to the corresponding amplitudes in QCD due to their supersymmetry expansion at one loop.