Observationally, an anti-correlation between the X-ray photon index Γ (obtained by fitting the X-ray spectrum between 0.5 and 10 keV with a single power law) and the X-ray luminosity L 0.5−10keV , i.e., a softening of the X-ray spectrum with decreasing L 0.5−10keV , is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of L 0.5−10keV ∼ 10 34 −10 36 erg s −1 . In this paper, we explain the observed anti-correlation between Γ and L 0.5−10keV within the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS. The ADAF model intrinsically predicts an anti-correlation between Γ and L 0.5−10keV . In the ADAF model, there is a key parameter, f th , which describes the fraction of the ADAF energy released at the surface of the NS as thermal emission to be scattered in the ADAF. We test the effect of f th on the anti-correlation between Γ and L 0.5−10keV . It is found that the value of f th can significantly affect the anti-correlation between Γ and L 0.5−10keV . Specifically, the anti-correlation between Γ and L 0.5−10keV becomes flatter with decreasing f th as taking f th = 0.1, 0.03, 0.01, 0.005, 0.003 and 0 respectively. By comparing with a sample of non-pulsating NS-LMXBs with well measured Γ and L 0.5−10keV , we find that indeed only a small value of 0.003 f th 0.1 is needed to match the observed anti-correlation between Γ and L 0.5−10keV . Finally, we argue that the small value of f th 0.1 derived in this paper further confirms our previous conclusion that the radiative efficiency of NSs with an ADAF accretion may not be as high as ǫ ∼ ṀGM R * / Ṁc 2 ∼ 0.2.