  We report the superconductivity in Ca-intercalated bilayer graphene
C$_6$CaC$_6$, the thinnest limit of Ca graphite intercalation compound. We
performed \textit{in situ} electrical transport measurements on pristine
bilayer graphene, C$_6$LiC$_6$ and C$_6$CaC$_6$ fabricated on SiC substrate
under zero and non-zero magnetic field. While both bilayer graphene and
C$_6$LiC$_6$ show non-superconducting behavior, C$_6$CaC$_6$ exhibits the
superconductivity with transition temperature ($T_{{\rm c}}$) of 4.0 K. The
observed $T_{{\rm c}}$ in C$_6$CaC$_6$ and the absence of superconductivity in
C$_6$LiC$_6$ show a good agreement with the theoretical prediction, suggesting
the importance of a free-electron-like metallic band at the Fermi level to
drive the superconductivity.
