Abstract: Noise and vibration are the two main factors that determine the stability of a mixed-flow pump during start-up process. In this paper, the shaft vibration and noise signals of the mixed-flow pump under different starting modes are collected, and then the noise and vibration characteristics of the pump are analyzed by the time-varying filtering-based empirical mode decomposition (TVF-EMD) method improved by the time-frequency analysis and triangulation topology optimization (TTAO) algorithm. Finally, stability assessment of the mixed-flow pump during the start-up process is conducted based on two-dimensional sample entropy. From the results, it can be found that the starting mode significantly affects the vibration shock characteristics of the shaft during the start-up process. And the average value of the energy entropy ratio of the shaft vibration under the starting Mode 2 (concave exponential function law) is the lowest, indicating that it can reduce the probability of vibration shock on the shaft during the start-up process. Meanwhile, the time scale of the high energy noise outside the pump is the shortest when the mixed-flow pump is started in Mode 2, indicating that Mode 2 can reduce the effect of high energy noise on the environment during the start-up process of the mixed-flow pump. When the mixed-flow pump is started in Mode 2, the two-dimensional sample entropy of the shaft vibration and noise signal is the lowest, indicating that the stability of the mixed-flow pump is the best when it is started in Mode 2.