Current gravitational waveform models used by detection data analysis have not included the effect of the moving speed of the sources relative to detector. Few works about the gravitational waveform problem for moving sources exist in the literature. And all of them have taken some approximations. Some of them just considered frequency shift. Some of them used slow speed approximation. In the current paper, we apply the precise Lorentz transformation of gravitational wave to generate the gravitational waveform for moving sources with any high speed. Our calculation is straightforward but without any approximation. That is to say our result is valid in the whole velocity range 0 ⩽ v < c which is only limited by the speed of light coming from general relativity itself. If only a waveform model of a rest source is given, our result can be applied directly to generate the waveform for the corresponding moving source with any high speed. Such waveform is valid for binary black hole coalescence happening extremely close to a super-massive black hole. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented in the current paper.