This paper studied the practical fault of motor vibration of a centrifugal compressor in one factory of Longyan. The analysis of the mechanism showed that the main factors affecting motor vibration were classified into mechanical, electrical and installation. Vibration signals were mostly periodic, quasi-periodic signals, or stationary random signals, and the fault feature frequency was related to the speed of the rotor, equal to the rotor rotating frequency and frequency doubling or frequency demultiplication. Based on the vibration differential equation, a mathematical calculation model of critical speed of motor vibration was established, and the analysis showed that motor vibration fault was due to the close of work speed to critical speed. By decreasing the shaft diameter, the first order critical speed become lowly, and the motor vibration fault had been eliminated.