In this work, we propose a new moving frame FDTD method based on the use of transformation optics (TO). Using TO, the time dependent Maxwell's equations are invariant but become magneto-electric in the moving frame and can be solved by a magneto-electric Maxwell solver. Previous proposed moving frame FDTD methods, such as the Lagrangian frame FDTD method, only transform the independent variables of the Maxwells equations that lead to instability due to numerical discretization of the additional advection terms introduced by the transformation and the PML boundary. In contrast, our method transform dependent and independent variables of the Maxwells equations to obtain an invariant form (no additional advection terms are introduced) so that instability problem is avoided. Numerical examples are presented to test the performance of our method.