The electronic and optical properties of 2D Cu2Si and Cu2Si:Ti are investigated based on the density functional theory (DFT) using the FP-LAPW method and GGA approximation. The 2D Cu2Si has metallic and non magnetic properties, whereas adding Ti impurity to its structure changes the electronic behavior to the half-metallic with 3.256μB magnetic moment. The optical transition is not occurred in the infrared and visible area for the 2D Cu2Si in x-direction and by adding Ti atom, the real part of dielectric function in the x-direction, Re (ε(ω))x is reached to a Dirac peak at this energy range. Moreover, the absorption gap tends to zero in x-direction of the 2D Cu2Si:Ti.