  Inspired by the newly observed $D_{sJ}(3040)^+$ state, in this work we
systemically study the two-body strong decays of P-wave charmed-strange mesons
with the first radial excitation. Under the assignment of $1^{+}(j^P=1/2^+)$,
i.e. the first radial excitation of $D_{s1}(2460)^+$, we find that the width of
$D_{sJ}(3040)^+$ is close to the lower limit of the BaBar measurement. This
indicates that it is reasonable to interpret $D_{sJ}(3040)^+$ as the first
radial excitation of $D_{s1}(2460)^+$. Our calculation further predicts that
$0^-+1^-$ channels e.g. $D^+K^{*0}$, $D^0 K^{*+}$ and $D_s^+\phi$ are important
for the search for $D_{sJ}(3040)^+$. To help future experiments finding the
remaining three P-wave charmed-strange mesons with the first radial excitation,
we present the predictions for the strong decays of these three P-wave
charmed-strange mesons.
