The dynamic response of curved steel beams has long been a research focus in curved bridges. The formula for the dynamic response under a moving load was derived according to the basic principles of the precise integration method. Combined with the necessary conditions of this method, the stiffness matrix of a variable-curvature beam was obtained using matrix inversion, and the mass matrix of the structure was obtained using the concentrated mass method. The dynamic response of the structure was obtained by applying moving loads and masses at different speeds to the curved beam. Finite element simulation and laboratory curved-beam models of the variable-curvature steel beam were established. By comparing the laboratory measurement results against the theoretical data obtained in this study, we propose that our theory has practical engineering significance. It can be used as a theoretical basis for the study of variable curvature steel beam structures and for guiding the construction of curved beams.