Studies show that operating stress and natural frequency of the turbocharger impeller are two key parameters that affect the service life of the turbocharger. In this regard, NREC and ANSYS software are utilized in the present study to design impellers and calculate the impeller stress, natural frequency, and the inertia moment of the impeller for each baseline impeller and their modifications. Furthermore, modal tests are carried out to verify the simulation results. Finally, the compressor characteristic maps before and after the blade gradient angle optimization are compared. Obtained results show that compared with the cantilever length, the blade thickness has a remarkable influence on the blade gradient angle. Moreover, it is found that the correlation between the blade gradient angle and the first-order frequency multiplication ratio is linear. As the blade gradient angle increases, the maximum stress at the blade root of the compressor initially decreases and then increases. The value of the blade gradient angle varies within the range of 2.288°–3.955°. Moreover, the closer the gradient angle to 3.26°, the smaller the maximum equivalent stress of the impeller, and the higher the impeller strength. The greater the thickness of the blade, the longer the cantilever length of the impeller, and the greater the inertia moment. Optimizing the blade gradient angle can improve the efficiency of the compressor without changing the pressure ratio and flow rate. It should be indicated that error between the results from the simulation and the experiment is within the range 1.736%–1.254%. Therefore, the calculation results are reliable. It is concluded that the regular pattern of the blade gradient angle affects the compressor impeller stress and its natural frequency. The present article is expected to provide a helpful theoretical basis for designing an optimized compressor impeller.