We study the mass spectra of the $N\mathrm{\ensuremath{\Omega}}$ dibaryons in the $^{3}{S}_{1}$ and $^{5}{S}_{2}$ channels with ${J}^{P}={1}^{+}$ and ${2}^{+}$, respectively, by using the method of QCD sum rules. We construct two dibaryon interpolating currents in the molecular picture and calculate their correlation functions and spectral densities up to dimension-16 condensates. Our results indicate that there may exist an $N\mathrm{\ensuremath{\Omega}}$ dibaryon bound state in the $^{5}{S}_{2}$ channel with a binding energy of about 21 MeV. The masses of the $^{3}{S}_{1}$ $N\mathrm{\ensuremath{\Omega}}$ dibaryons with ${J}^{P}={1}^{+}$ are predicted to be higher than the $N\mathrm{\ensuremath{\Omega}}$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ thresholds and thus, can decay into these final states directly in S wave. The $N\mathrm{\ensuremath{\Omega}}(^{5}{S}_{2})$ dibaryon bound state can decay into the octet-octet final states $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ and $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Xi}}$ in D wave via the quark rearrangement mechanism. The existence of these $N\mathrm{\ensuremath{\Omega}}$ dibaryons may be identified in the relativistic heavy-ion collision experiments in the future.