  The charm semileptonic decays $D^+\to\eta e^+\nu_{e}$ and
$D^+\to\eta'e^+\nu_{e}$ are studied with a sample of $e^+e^-$ collision data
corresponding to an integrated luminosity of 2.93 fb$^{-1}$ collected at
$\sqrt{s}$ = 3.773 GeV with the BESIII detector. We measure the branching
fractions for $D^+\to\eta e^+\nu_{e}$ to be
$(10.74\pm0.81\pm0.51)\times10^{-4}$, and for $D^+\to\eta'e^+\nu_{e}$ to be
$(1.91\pm0.51\pm0.13)\times10^{-4}$, where the uncertainties are statistical
and systematic, respectively. In addition, we perform a measurement of the form
factor in the decay $D^+\to\eta e^+\nu_{e}$. All the results are consistent
with those obtained by the CLEO-c experiment.
