  The specific heat $C(T)$ of new iron-based high-$T_c$ superconductor
SmO$_{1-x}$F$_x$FeAs ($0 \leq x \leq 0.2$) was systematically studied. For
undoped $x$ = 0 sample, a specific heat jump was observed at 130 K. This is
attributed to the structural or spin-density-wave (SDW) transition, which also
manifests on resistivity as a rapid drop. However, this jump disappears with
slight F doping in $x$ = 0.05 sample, although the resistivity drop still
exists. The specific heat $C/T$ shows clear anomaly near $T_c$ for $x$ = 0.15
and 0.20 superconducting samples. Such anomaly has been absent in
LaO$_{1-x}$F$_x$FeAs. For the parent compound SmOFeAs, $C(T)$ shows a sharp
peak at 4.6 K, and with electron doping in $x$ = 0.15 sample, this peak shifts
to 3.7 K. It is interpreted that such a sharp peak results from the
antiferromagnetic ordering of Sm$^{3+}$ ions in this system, which mimics the
electron-doped high-$T_c$ cuprate Sm$_{2-x}$Ce$_x$CuO$_{4-\delta}$.
