  In this paper, the $D\to P(\pi, K)$ helicity form factors (HFFs) are studied
by applying the QCD light-cone sum rule (LCSR) approach. The calculation
accuracy is up to next-to-leading order (NLO) gluon radiation correction of
twist-(2,3) distribution amplitude. The resultant HFFs at large recoil point
are ${\cal P}_{t,0}^\pi(0) = 0.688^{+0.020}_{-0.024}$, ${\cal
P}_{t,0}^K(0)=0.780^{+0.024}_{-0.029}$. In which, the contributions from three
particles of the leading order (LO) are so small that can be safely neglected,
and the maximal contribution of the NLO gluon radiation correction for ${\cal
P}_{t,0}^{\pi,K}(0)$ is less than $3\%$. After extrapolating the LCSR
predictions for these HFFs to whole $q^2$-region, we obtain the decay widths
for semileptonic decay processes $D\to P\ell\nu_\ell$, which are consistent
with BES-III collaboration predictions within errors. After considering the
$D^{+}/D^{0}$-meson lifetime, we give the branching fractions of $D\to
P\ell\nu_\ell$ with $\ell = e, \mu$, our predictions also agree with BES-III
collaboration within errors, especially for $D\to \pi \ell\nu_\ell$ decay
process. Finally, we present the forward-backward asymmetry ${\cal A}_{\rm
FB}^\ell(q^2)$ and lepton convexity parameter ${\cal C}_F^\ell(q^2)$, and
further calculate the mean value of these two observations $\langle{\cal
A}_{\rm FB}^\ell\rangle$ and $\langle{\cal C}_F^\ell\rangle$, which may provide
a way to test those HFFs in future experiments.
