This paper presents the local bifurcation analysis of the dynamic behavior for a centrifugal compressor. It is known that the surge phenomenon in compressor dynamics might occur at high pressure rise operation. Under such an operation, slight variation of the driving torque and/or the throttle opening might sharply reduce the compressor efficiency and even damage the system. Local bifurcation analysis of the centrifugal compressor system presented in this paper reveals the existence conditions of surge phenomenon. Bifurcation scenarios of compressor dynamics are also obtained with respect to the variation of driving torque and/or throttle opening, which provide a guide to determine the occurrence of nonlinear phenomena and reveal the stability limit for the compressor dynamics in the practical application. Numerical results demonstrate the linkage between nonlinear dynamical behavior and bifurcation phenomena.