For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.