A thermal soft X-ray component is often detected in low-level accreting neutron stars (NSs), but is not detected in low-level accreting stellar-mass black holes (BHs). In this paper, we investigate the origin of such a thermal soft X-ray component in the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around NSs. It is assumed that a fraction, $f_{rm th}$, of the energy transferred onto the surface of the NS is thermalized at the surface of the NS as the soft photons to be scattered in the ADAF. We self-consistently calculate the structure and the corresponding emergent spectrum of the ADAF by considering the radiative coupling between the soft photons from the surface of the NS and the ADAF itself. We show that the Compton $y$-parameter of the ADAF for NSs is systematically lower than that of BHs. Meanwhile, we find that the temperature of the thermal soft X-ray component in NSs decreases with decreasing mass accretion rate, which is qualitatively consistent with observations. We test the effect of $f_{rm th}$ on the structure, as well as the emergent spectrum of the ADAF. It is found that a change of $f_{rm th}$ can significantly change the temperature of the thermal soft X-ray component as well as the spectral slope in hard X-rays. Finally, it is suggested that the value of $f_{rm th}$ can be constrained by fitting the high-quality X-ray data, such as the $it XMM$-$it Newton$ spectrum between 0.5-10 keV in the future work.
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