A nonlinear tomographic approach for microwave imaging of dielectrics buried under a rough surface is presented. It has been made possible to efficiently apply the contrast-source-inversion method, which is proven to be one of the most successful nonlinear inversion techniques when the Green's function of the background medium is available, to the given imaging problem. This has been achieved through the application of the buried object approach (BOA) which enables the calculation of the Green's function of layered media with rough interfaces by considering the roughness as a series of objects located alternately on both sides of a planar interface between two half spaces. Furthermore, the calculation of the Green's function of the two-layered medium with a planar interface required in the BOA has been accelerated through an adaptation of the two-level discrete complex image method. By making use of the strength of nonlinear inversion and fast and accurate computation of the Green's function of the layered media with rough interface, superior results have been achieved in a feasible computational time for dielectrics having constitutive parameters in a considerably wide range even if they are inhomogeneous or buried under substantially large rough surfaces.