  When neutrons star low-mass X-ray binaries (NS-LMXBs) are in the low-level
accretion regime (i.e., $L_{\rm X}\lesssim 10^{36}\ \rm erg\ s^{-1}$), the
accretion flow in the inner region around the NS is expected to be existed in
the form of the hot accretion flow, e.g., the advection-dominated accretion
flow (ADAF) as that in black hole X-ray binaries. Following our previous
studies in Qiao $\&$ Liu 2020a and 2020b on the ADAF accretion around NSs, in
this paper, we investigate the radiative efficiency of NSs with an ADAF
accretion in detail, showing that the radiative efficiency of NSs with an ADAF
accretion is much lower than that of $\epsilon \sim {\dot M GM\over
R_{*}}/{\dot M c^2}\sim 0.2$ despite the existence of the hard surface. As a
result, given a X-ray luminosity $L_{\rm X}$ (e.g., between 0.5 and 10 keV),
$\dot M$ calculated by $\dot M=L_{\rm X}{R_{*}\over {GM}}$ is lower than the
real $\dot M$ calculated within the framework of the ADAF accretion. The real
$\dot M$ can be more than two orders of magnitude higher than that of
calculated by $\dot M=L_{\rm X}{R_{*}\over {GM}}$ with appropriate model
parameters. Finally, we discuss that if applicable, the model of ADAF accretion
around a NS can be applied to explain the observed millisecond X-ray pulsation
in some NS-LMXBs (such as PSR J1023+0038, XSS J12270-4859 and IGR J17379-3747)
at a lower X-ray luminosity of a few times of $10^{33}\ \rm erg\ s^{-1}$, since
at this X-ray luminosity the calculated $\dot M$ with the model of ADAF
accretion can be high enough to drive a fraction of the matter in the accretion
flow to be channelled onto the surface of the NS forming the X-ray pulsation.
