Integrally geared centrifugal compressors have found wide applications in air separation plants and the petrochemical industry because they can be readily designed to run at a higher efficiency than in-line compressors. Many of these compressors with multiple stages are designed to meet the demands for high power and high speed applications with high efficiency and high reliability. These requirements are challenges for their rotordynamic designs. Some compressors may experience excessive synchronous or subsynchronous vibrations during commissioning or in a short period of service. This study starts with discussing the vibration characteristics of a compressor pinion-bearing system, including undamped critical speeds, unbalance responses, and rotordynamic stability. To improve the rotordynamic performance, a systematic and feasible approach for modifying a rotordynamic design has been proposed. It has been showed that damped modes at an operating speed are key indicators of the rotordynamic performance. The sensitivities of damped modes to main design variables, i.e. bearing geometry, shaft geometry and impeller mass properties, are thoroughly examined. A procedure for design modification is proposed for general guidance. The feasibility and effectiveness of this method have been demonstrated in the modification of a pinion-bearing system. In addition, this paper also proposes a method to evaluate the torsional natural frequencies of an equivalent pinion model and briefly discusses the application of optimal design methodology to the rotordynamic design modification.