The submillimetre-wave spectrum of C3O (X^1^{Sigma}^+^) has been investigated in the laboratory using a source-modulation microwave spectrometer equipped with a gas-phase flow pyrolysis system for the production of unstable chemical species. C3O was produced by thermal decomposition of fumaryl chloride at 900{deg}C. Thirty-seven new rotational transitions were observed in the frequency range 307-740GHz for the ground vibrational state, reaching a J quantum number as high as 76. Additionally, new millimetre-wave and submillimetre-wave lines were recorded for the bending fundamental v5=1, and for its overtone v5=2 and v5=3 whose rotational spectra have been identified for the first time. The new laboratory measurements provide much improved rest frequencies in the submillimetre spectral region for the ground state spectra of C3O, and for the first levels of its low-energy v5 vibrational ladder, useful for the radioastronomical identification of the irrotational lines in the ISM.