One-flavour QCD - a gauge theory with SU(3) colour gauge group and a fermion in the fundamental representation - is studied by Monte Carlo simulations. The mass spectrum of hadronic bound states is investigated in a volume with extensions of L ~ 4.4r_0 (~2.2fm) at two different lattice spacings: a ~ 0.37r_0 (~0.19fm) and a ~ 0.27r_0 (~0.13fm). The lattice action is Symanzik tree-level-improved Wilson action for the gauge field and (unimproved) Wilson action for the fermion.