An approximate computational model of an electromagnetic (EM) pulse excited thin-wire antenna is developed. The presented solution methodology is based on the Cagniard-deHoop method of moments (CdH-MoM) and Hallén's approximation of the thin-wire model. It is shown that the proposed time-domain (TD) solution leads to an inversion-free, efficient updating procedure that mitigates the marching-on-in-time accumulation error. An illustrative numerical example demonstrates the validity of the proposed model.