In this paper, we suggest an anticipating projective response scheme in coupled dynamical systems, from which a large class of different drive-response systems can be constructed by choosing different functions and changing the scaling factor. A specific case of the scheme, which is named the accelerative anticipating projective response scheme, is studied in detail. In this specific scheme, the amplitudes of the drive and response systems synchronize up to a scaling factor and the response system evolves with a faster speed. Further, the robustness of this scheme is proved under the existence of the small disturbance of the driving term, interference of the driving signal and parameter mismatches.