In this paper,a silicon-graphene electro-optical half-adder is presented,which is composed of three cascaded Mac h-Zehnder interferometer(MZI)-based optical switches. For each phase shifter,a silicon slot waveguide embedded with graphene flakes i s adopted.The modal effective index of the silicon slot waveguide embedded with graphene flakes varies accordi ng to the carrier density in graphene.To achieve switching function,an electrical signal is applied to tune the Fermi levels of graphene flakes leading to the variation of modal effective index.Simulation results show that t he worst crosstalk of the Mach-Zehnder-based optical switch is －21.57dB and the insertion loss is lower than 0.109dB withi n a bandwidth from 1520nm to 1600nm when the chemical potential of graphene swiches between 0.50eV and 0.64eV. The designed silicon-gra phene electro-optical half-adder with the operation speed of 10Gbit/s has an extinction ratio larger than 41.05dB at an operating wavelength of 1550nm.