This paper presents a method for the shape optimization of an acoustic horn with respect to the impedance matching property based on the discrete multimodal method. The method models the horn as a series of short cylinders and takes mode coupling across the discontinuities into account. The optimization employs a gradient-based algorithm, and allows for analytical derivation of the objective function and its gradient in a numerically workable manner. A case study followed with an experimental validation is presented. With appropriate parameter settings, the method is capable of rapidly finding a smooth and convex horn design that behaves like a high-pass radiator with near-ideal wideband transmission in small dimensions.