The extended Born approximation (ExBorn) has been shown an efficient formulation in the electromagnetic (EM) scattering by dielectric objects in both free-space and air-earth half-space problems. In most cases, ExBorn is much more accurate than the conventional Born approximation at low frequencies. When the frequency is high or the contrast of dielectric objects is large, however, the ExBorn approximation becomes inaccurate. In this paper, new approximations are proposed for the EM scattering by dielectric objects buried in a lossy earth, which are also suitable for the case of free space. It has been shown that the zeroth-order form of new approximations is completely equivalent to ExBorn. Hence, high-order approximations can be regarded as high-order ExBorn. Closed-form formulations are derived for the new approximations. Using the fast Fourier transform (FFT), these formulations can be implemented efficiently at a cost of log, where is the number of unknowns and is a small number. Numerical simulations show that high-order ExBorn approximations are much more accurate than the ExBorn approximation.