A hybrid algorithm of time domain integral equation (TDIE) and time domain Kirchhof approximation (TDKA) is proposed to compute the TM transient scattering from a 2-dimensional (2D) perfectly conducting (PEC) target above 2D PEC randomly rough surface. Explicit and implicit procedures of Marching-on-in-time (MOT) are developed, respectively. TDKA is applied to the rough surface while TDIE is applied to the target, and the mixed iteration of TDIE/TDKA is introduced to take into account the interactions between the target and the rough surface. In numerical examples, both bent strip (open structure) and cylinder (closed struc- ture) are considered and numerical results present the target surface current response and the far scattered electric field response, which are compared with those obtained from whole TDIE. Numerical results demonstrate the efficiency and the accuracy of the hybrid algorithm. Still in numerical examples, the influence on the far scattered electric field caused by the target is discussed.