  We present a QCD sum rule analysis for the newly observed resonance
$X_{c}(3250)$ by assuming it as a $D_{0}^{*}(2400)N$ molecular state.
Technically, contributions of operators up to dimension 12 are included in the
operator product expansion (OPE). We find that it is difficult to find the
conventional OPE convergence in this work. By trying releasing the rigid OPE
convergence criterion, one could find that the OPE convergence is still under
control in the present work and the numerical result for $D_{0}^{*}(2400)N$
state is $3.18\pm0.51 {GeV}$, which is in agreement with the experimental data
of $X_{c}(3250)$. In view of that the conventional OPE convergence is not
obtained here, thus only weak conclusions can be drawn regarding the
explanation of $X_{c}(3250)$ in terms of a $D_{0}^{*}(2400)N$ molecular state.
As a byproduct, the mass for the bottom counterpart $\bar{B}_{0}^{*}N$ state is
predicted to be $6.50\pm0.49 {GeV}$.
