The transient eddy current field is analytically modeled by applying inverse Laplace transform to pulsed eddy current testing. The closed-form solution to transient eddy current field in a complex domain is obtained by using the truncated region eigenfunction expansion (TREE) method and the theory of reflection and transmission of electromagnetic waves. After extensive algebraic transform, the poles of the developed model and corresponding residues are able to be calculated. As a result, partial fraction expansion can be used to split up the complicated complex-domain model into the forms that are listed in the Laplace Transform table. Therefore, it is easy to derive the time-domain solutions to transient eddy current field with step and exponential current excitations respectively. The derived time-domain model not only has some advantages in the sense of implementation and efficiency, but also removes the Gibbs phenomenon. Finally, the inverse Fourier transform of induced voltage in the probe is performed and the good agreement demonstrates the validity of the established model.