By　using　an　ab　initio　evolutionary　algorithm　structure　search,　low　enthalpy　criterion　as　well　as　stability　analysis,　we　have　found　that　cubic　Fm　(3)　over　barm　Ca2Si　can　be　achieved　under　a　negative　external　pressure,　and　the　cubic　phase　is　dynamically　and　mechanically　stable　at　ambient　conditions　and　high　pressure.　From　first-principle　hybrid　functional　calculations,　we　have　unraveled　the　direct　bandgap　nature　and　bandgap　variation　of　cubic　Fm　(3)　over　barm　Ca2Si　with　respective　to　pressure.　Moreover,　by　combining　with　Boltzmann　transport　theory　and　the　phonon　Boltzmann　transport　equation,　we　have　predicted　that　the　figure　of　merit　ZT　for　the　cubic　Fm　(3)　over　barm　Ca2Si　reaches　the　maximum　value　of　0.52　by　p-type　doping.　Our　results　provide　an　interesting　insight　and　feasible　guidelines　for　the　potential　applications　of　cubic　Fm　(3)　over　barm　Ca2Si　and　related　alkaline-　earth　metals　silicides　as　the　thermoelectric　materials　for　heat-electricity　energy　convertors.