There is the nonlinear phenomenon in the output signal of double-tube Coriolis mass flowmeter, which is mainly the frequency doubling signal. The source has been traced from the perspective of numerical analysis. In this article, the full parametric model built by ANSYS finite element analysis software is used to further evaluate the reliability of the numerical model through simulation experiments. By analyzing the influence of the excitation force on the nonlinear vibration of the measuring tube mass and the thickness of the measuring tube spacing plate, it proves that the measuring tube stiffness and the constraint stiffness have important effects on suppressing the nonlinear vibration. Then, the additional mass method is used to improve the local stiffness of the coupling system to suppress the nonlinear frequency doubling phenomenon. Results show that the improved local stiffness can effectively suppress and eliminate the nonlinear phenomenon. The nonlinear suppression experiments are carried out, and the results accord with the simulation analysis, which verifies the correctness of the theoretical research. This part of work provides theoretical support and technical guidance for further refining nonlinear suppression scheme and carrying out nonlinear suppression experiments. Combined with the specific measurement environment and measurement requirements, the nonlinear phenomenon can be suppressed or eliminated, as the next step of CMF optimization design basis.