Pressure can tune material's electronic properties and control its quantum state, making some systems present disconnected superconducting region as observed in iron chalcogenides and heavy fermion CeCu2Si2. For CaC6 superconductor (Tc of 11.5 K), applying pressure first Tc increases and then suppresses and the superconductivity of this compound is eventually disappeared at about 18 GPa. Here, we report a theoretical finding of the re-emergence of superconductivity in heavily compressed CaC6. The predicted phase III (space group Pmmn) with formation of carbon nanofoam is found to be stable at wide pressure range with a Tc up to 14.7 K at 78 GPa. Diamond-like carbon structure is adhered to the phase IV (Cmcm) for compressed CaC6 after 126 GPa, which has bad metallic behavior, indicating again departure from superconductivity. Re-emerged superconductivity in compressed CaC6 paves a new way to design new-type superconductor by inserting metal into nanoporous host lattice.