The interference fit between impeller and shaft assembly is one of the most important factors influencing the performance of the turbo unit in the design of turbocharger compressor. The assembly creates a complicated frictional contact problem in the interface of the mating parts. The existing of centrifugal force may cause the variation of the interference fit especially when the rotating speed is high. Therefore, a suitable fit tolerance needs to be considered in the structural design of turbocharger compressor. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading is used for the analysis. The FE parametric quadratic programming (PQP) method which was developed based on the parametric variational principle (PVP) is used for the analysis of the stress distribution of 3D frictional contact problem of impeller-shaft sleeve-shaft, and then, using the multi-level, multi-branch substructure technique of FE, makes it possible to precisely simulate complicated geometrical shapes of impeller and considerably enhances accuracy in numerical computation. The advantages of the parametric programming method as compared with the conventional ones are that the penalty factors can be cancelled and the solutions can be obtained directly without tedious iterative procedures such as general incremental iterative method. The effects of fit tolerance and rotating speed, the displacement and the contact pressure on the interference-fitting surfaces are discussed in detail in the numerical computation. A range of friction coefficients in the impeller-shaft sleeve and shaft sleeve-shaft contact interfaces is investigated in order to represent the mechanical behaviors of the structure due to the change of the interface characteristic. To decrease the difficulty of the assembling process and make sure the safety of the working state, the suitable amount of the interference is studied so that the interface can have adequate contact pressure under full load. To assure quality of press-fitting, the amount of interference between the shaft sleeve and shaft by press-fitting should be controlled strictly to avoid the rapid increase of the contact stress. The results obtained play a referential role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers. The study provides also an effective approach which achieves more reliable interference-fitted connections and more precise assembly accuracy with lower manufacturing cost in the structural design.