In this study, a Si–graphene composite, which is composed of nano Si particles and nano-sized multi-layer graphene particles, and micro-sized multi-layer graphene plate conductor, was used as the anode for Li-ion battery. The Si–graphene electrode showed the high capacity and stable cyclability at charge/discharge rate of C/2 in half cell tests. Nickel cobalt aluminum material (NCA) was used as a cathode in the full cell to evaluate the practicality of the new Si–graphene material. Although the Si–graphene anode has more capacity than the NCA cathode in this designed full cell, the Si–graphene anode had a greater effect on the full-cell performance due to its large initial irreversible capacity loss and continuous SEI formation during cycling. When fluoro-ethylene carbonate was added to the electrolyte, the cyclability of the full cell was much improved due to less SEI formation, which was confirmed by the decreases in the 1st irreversible capacity loss, overpotential for the 1st lithiation, and the resistance of the SEI.