The evolutions of noise characteristics of the pump have significant implications for monitoring the stability of the mixed-flow pump (MFP) start-up process. To investigate the variations in noise characteristics under different start-up modes and start-up times, the noise, shaft vibration and pressure pulsation of MFP under linear and nonlinear start-up modes were collected by an acoustic and vibration experimental system. Subsequently, an analysis was conducted based on acoustic signal processing methods. The results show that the high-amplitude sound pressure under different start-up modes appears in the later stage of start-up, and the time for the high-amplitude noise region to appear is the shortest under the concave exponential (CCEF) start-up mode. The shock noise under the CCEF start-up mode is relatively small, indicating that this start-up mode is conducive to avoiding severe mechanical collisions and shocks during the start-up process. The highest A-weighted sound pressure level (SPL) of the noise under different start-up modes appears at the center frequency of 250 Hz, and the CCEF start-up mode brings about the smallest total effective SPL. Adopting the CCEF start-up mode and extending the start-up time is beneficial to avoid severe mechanical collisions, reduce the SPL in each frequency band, and weaken the continuous impact of noise on the environment during the MFP start-up process. In addition, CCEF start-up modes can effectively reduce the tone of the noise during the start-up of the MFP.