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In this paper we propose and analyze a method to control the group velocity of an ultrafast pulse based on the electro-optic effect and quadratic cascading nonlinearity. The evolution of the input pulse in a quasi-phase matching (QPM) grating behaves like quadratic slow light solitons, whose group delay can be tuned by changing the applied external electric field along the z-axis of the crystal. Our simulation also shows that an asymmetric QPM domain structure is necessary for the group delay to be tunable by an external electric field. A potential application in dispersion management when constructing a delay line in high-speed system is suggested at the end of discussion.