In this letter, a novel time-domain wave propagator, based on the transmission line matrix (TLM) technique, is introduced. A two-dimensional (2-D) TLM algorithm is modified and the sliding window technique is applied to analyze ground wave propagation characteristics. The longitudinal propagation region over earth's surface is covered by a finite-size TLM computation space, as if the space slides from source to observation point. A short pulse is injected into the TLM computation space as a vertical initial source distribution near the left end and is traced within an adjustable window while propagating toward right. Perfectly matched layer (PML) blocks on the left, top and right terminate the TLM computation space to simulate semi-open propagation region, The ground at the bottom is a perfectly electrical conductor (PEC). The PML blocks absorb field components that scatter back and top. The ground wave components (i.e., the direct, ground-reflected and surface waves) are traced longitudinally toward right. Transient propagation can be observed at any range/altitude by accumulating time history of the desired field components and any steady-state vertical and/or horizontal field profile at a desired frequency can be extracted by applying off-line discrete Fourier transformation (DFT).