Although the offset-elliptical journal bearings (OEJBs) are widely used in industry, there are few researches on the OEJBs, especially under the conditions of journal misalignment and sudden load. To overcome such deficiency, the dynamic response of misaligned OEJBs subjected to the dynamic load has been studied in this paper. Based on the Reynolds equation, Euler equation, and kinetic equations, a hydrodynamic model is developed and validated to conduct the transient analysis for the OEJBs. Moreover, the modified film thickness of the misaligned OEJB is given. The partial derivative method and the finite difference method are adopted to solve the lubrication equations. The correlations of bearing characteristics such as the minimum film thickness, maximum film pressure, journal orbits, and time-varying dynamic coefficients with the misalignment and dynamic load are studied. In addition, the effects of the misalignment, rotating speed, and clearance ratio on the transient performance of OEJBs under the dynamic load are discussed in detail. The results indicate that the journal misalignment and dynamic load have a significant impact on the transient performance of OEJBs. The decrease of the film thickness caused by the journal misalignment can be aggravated by the suddenly applied load. The proposed model can provide theoretical fundament in the design and monitoring of the dynamically loaded bearing-rotor system.