We apply for the first time renormalization group theory to a system with a first-order phase transition between opposite magnetizations driven linearly by an external magnetic field.The system is described by the large--N model with continuous symmetry and its dynamics is governed by the time-dependent Ginzburg-Landau model. We show explicitly that the driven transition is also governed by the zero-temperature fixed point

and obtain novel dynamic scaling forms for the magnetization and the structure factor. From these relations the scaling form for the area of hysteresis loop with corrections follows naturally. Numerical results agree excellently with the theoretical predictions.