Graphene is an ideal two-dimensional crystal with the advantages of high conductivity, unique physical and chemical properties, and high specific surface area. Especially, because of its super excellent electronic properties, graphene may substitute the traditional semiconductor silicon material and carbon nanotube, thus creating a new nanoscale electronic device. In addition, multilayer graphene with ultra-wide spectral absorption characteristics and unique photoelectric properties is an ideal material for photovoltaic devices. However, the zero band gap and semi-metality of graphene both limit its application in space detectors such as the microelectronic industries and satellites. Opening and regulating the graphene band gap by physical methods has become one of the key means to further expand its applications. Research work has shown that the doping of elements can significantly change the electronic structure of graphene, thereby regulating the optical properties of graphene. In order to provide an insight into electronic properties of graphene and tune its electronic band structure and optical properties effectively, electronic and optical properties of Ni-doped multi-layer graphene are studied and a number of interesting results are obtained. The calculation are carried out by the CASTEP tool in Materials Studio software based on the first-principles of ultrasoft pseudopotential of density functional theory. The models of three typical doping positions relative to carbon atoms are constructed. After structural optimization, it is obtained that " above the center of two carbon atoms” is the most stable doping structure. By using the method of local density approximation, the band structure, density of states, dielectric constant, reflectivity and refractive index of the models are calculated. The results show that an enhanced energy band gap can be achieved after nickel-doping, and reach up to 0.604 eV. Besides, peaked phenomenon of density of states at Femi level can be observed, which is accomplished by enhancing the plasma energy. Furthermore, the calculations show that the imaginary part of permittivity and refractive index increase after nickel-doping, suggesting that the optical absorbing performance is improved. All these results provide theoretical guidance for further exploring the optical properties of graphene.