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The sodium monoxide radical (NaO) is observed in night glow in the Earth'smesosphere and likely has astronomical importance. This study concerns theoptical transitions within the ground X $^2\Pi$ state and to the very low-lying($T_{\textrm e}\approx 2000$ cm$^{-1}$) excited A $^2\Sigma^+$ state. A linelist consisting of rovibronic term values, allowed electric dipole transitions,Einstein coefficients, and partition functions for varying temperature areproduced due to a variational solution of the coupled-channel Schr\"{o}dingerequations using the program \Duo. MRCI \textit{ab initio} calculationscharacterising the potential energy curves of the both states, spin-orbit and$L$-uncoupling non-adiabatic matrix elements, as well as permanent andtransition dipole moments were integral in formation of the finaldeperturbation model. \textit{Ab initio} potential energy curves arerepresented in the analytical Extended-Morse-Oscillator form and refined, alongwith the spin-orbit and $L$-uncoupling functions, by least-squares fitting tothe available spectroscopic data. The input experimental data consisted of purerotational transitions within the fine structure components of the X $^2\Pi$state for $v''\in [0,3]$ vibrational levels as well as the rovibronic A$^2\Sigma^+(v'=0) \leftarrow$ X $^2\Pi(v''=0)$ transitions, both with limitedcoverage over rotational excitation. The lack of data detailing the vibrationalstructure of the X and A states prompts a request for further experimentalstudy of higher excited levels which would provide a robust spectroscopicmodel. The NaO NaOUCMe line list is available via www.exomol.com and the CDSdatabase.

ExoMol molecular line lists -- XLIII: Rovibronic molecular line list the low-lying two states of NaO