We present an analysis of the far-infrared and submillimetre molecular emission-line spectrum of the luminous M-supergiant VY CMa, observed with the Spectral and Photometric Imaging Receiver (SPIRE) and Photodetector Array Camera and Spectrometer for Herschel spectrometers aboard the Herschel Space Observatory. Over 260 emission lines were detected in the 190-650{mu}m SPIRE Fourier Transform Spectrometer spectra, with one-third of the observed lines being attributable to H_2_O. Other detected species include CO, ^13^CO, H_2_O, SiO, HCN, SO, SO2, CS, H_2_S and NH_3_. Our model fits to the observed ^12^CO and ^13^CO line intensities yield a ^12^C/^13^C ratio of 5.6+/-1.8, consistent with measurements of this ratio for other M-supergiants, but significantly lower than previously estimated for VY CMa from observations of lower-J lines. The spectral line energy distribution for 20 SiO rotational lines shows two temperature components: a hot component at ~1000K, which we attribute to the stellar atmosphere and inner wind, plus a cooler ~200K component, which we attribute to an origin in the outer circumstellar envelope. We fit the line fluxes of ^12^CO, ^13^CO, H_2_O and SiO, using the smmol non-local thermodynamic equilibrium (LTE) line transfer code, with a mass-loss rate of 1.85x10^-4^M_{sun}_/yr between 9R* and 350R*. We also fit the observed line fluxes of ^12^CO, ^13^CO, H_2_O and SiO with smmol non-LTE line radiative transfer code, along with a mass-loss rate of 1.85x10^-4^M_{sun}_/yr. To fit the high rotational lines of CO and H_2_O, the model required a rather flat temperature distribution inside the dust condensation radius, attributed to the high H_2_O opacity. Beyond the dust condensation radius the gas temperature is fitted best by an r-0.5 radial dependence, consistent with the coolant lines becoming optically thin. Our H_2_O emission-line fits are consistent with an ortho:para ratio of 3 in the outflow.