The Time-Domain-Integral-Equation (TDIE) method is proposed to analyze transient scattering interaction between a two-dimensional infinitely long conducting target with an arbitrary cross section and a one-dimensional rough surface. Based on the electric-field-integral-equation in time domain, the explicit and implicit solutions of MOT (Marching-on-time) are derived and presented. The current response at the center of the rough surface and the far electric field response with time in the composite model are calculated and analyzed. The numerical results are compared and verified with those obtained by conventional MOM-IDFT (Method of Moment-inverse discrete Fourier transform). Finally, the influence of the size, the location of the target and the incident angle on the current response and the far electric fields response are discussed in detail. rough surface, PEC target, Time-Domain-Integral-Equation (TDIE), transient scatteringElectromagnetic (EM) scattering from the target above a rough surface has attracted much interest during recent years. It has been the subject of intensive investigation over the past several decades for its extensive applications in a number of important research areas, such as radar surveillance and target identification. Up to now, most of the studies are based on the frequency-domain methods [1][2][3][4][5][6] , such as the method of moments (MOM), sparse matrix canonical grid method (SMCGM), generalized FBM (GFBM), and FBM spectrum acceleration algorithm (FBM/SAA). In the last few decades, with the extensive applications of impulse technique in microwave, millimeter wave communication and radar surveillance, the study of the EM fields in the time domain has been extensively investigated. The time-domain methods applied to the rough surface may give the EM field distributions at every sampling time, which shows us the development of the EM fields with time. The study of EM scattering problem in the time domain has been dominated by the differential equation methods, such as FDTD [7] with the advantage of simple and easy implementation. In fact, TDIE, FDTD and MOM were proposed at the meantime in the 1960s; however, TDIE developed slowly in the subsequent 30 years and its applications were far from extensive. The study of TDIE was rapidly developed [8][9][10][11][12] in the 1990s for the predominant advantages such as no artificial edge conditions [13,14] in the implementation. The RWG was successfully applied to TDIE by Rynn [7] and Rao et al. [15,16] , and subsequently, the MOT algorithm in TDIE was generalized in ref.[17] by Rao. At present, TDIE has been extensively applied in the transient scattered fields of a deterministic target, whereas there are few reports about its application on the composite transient scattering from the rough surface and the target above it at home and