A Yang-Mills-type quadratic gravity model is considered in the framework of a five-dimensional Kaluza-Klein theory. Field equations and stress-energy tensors are presented in differential forms. Afive-dimensional classical Kaluza-Klein metric ansatz is investigated, which consists of a four-dimensional plane-fronted gravitational wave with parallel rays as its sub-metric along with a non-trivial dilaton and gauge fields. It is found that the solution is equivalent to plane-gravitational waves in terms of a spin-0 dilaton and a spin-1 photon. Some special cases are discussed, and it is shown that only the plane-electromagnetic waves with helicity-1 states carried non-zero energy-momentum.