Abstract: Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied. The Hilbert space and an important inequalitywere obtained using interior product of the Fourier transform on a quickly decaying functional space. The existence theorem of the solutions for the initial value problemwas proved using Schauder fixed-point theorem under some assumed conditions of known function.