  We systematically study the semileptonic decay process of $ D\rightarrow S,A
l\bar{\nu_{l}}(l=e,\mu)$ by light-cone sum rules (LCSR) with chiral currents,
calculate the form factors containing only the contribution of the leading
twist light-cone distribution amplitudes (LCDAs). For scalar mesons
$a_{0}(980)$ and $a_{0}(1450)$, we take them as $q\bar{q}$ states. For
axial-vector meson, we study $a_{1}(1260)( 1^{3}p^{1})$ and $b_{1}(1235)(
1^{1}p^{1})$. Based on the results of these form factors, we further present
the branching ratios of these semileptonic decay processes. The numerical
results for $ D\rightarrow a_{0}(980), b_{1}(1235)l\bar{\nu_{l}} $ are in good
agreement with experiments and that for $ D\rightarrow
a_{0}(1450)l\bar{\nu_{l}}$ process are expected to be tested experimentally in
the future.
