This paper presents a theoretical method to estimate the pulse radiation characteristics of Vivaldi antennas. Based on the surface current distribution and the ultra-wideband radiation principle, Vivaldi antenna is equivalently modeled as a dipole array, and the pulse radiation characteristics of a single Vivaldi antenna are brought out utilizing the spatial superposition approach. Then, the influences and results of the Vivaldi antenna pulse characteristics prediction with different construction ways of the dipole array and element numbers are furthermore investigated. Next, a quadratic spatial superposition technique is employed to complete the theoretical prediction for time-domain radiation characteristics of Vivaldi antenna arrays. Experiments and simulations are conducted separately to verify the proposed method for both single Vivaldi antenna and array. The validated results demonstrate that the dipole array-based theoretical prediction method can effectively capture the pulse radiation characteristics for both individual Vivaldi antenna and array operating in different modes, thereby addressing challenges associated with estimating radiation characteristics in ultra-wideband pulse applications.