The number of blades is one of the main geometric parameters of centrifugal pump, which is widely used in agricultural machinery, and it has an important influence on the vibration and noise of centrifugal pumps. Both vibration and noise can affect the centrifugal pump performance and its life, and the sources of vibration and noise may lie in hydraulic or mechanical aspects. In fact, most previous works for vibration and noise of centrifugal pumps mostly focused on theoretical and experimental studies. However, these studies seem to simulate the volute and impeller interactions only, without consideration of the leakage flow paths. The leakage flow paths between the rotating impeller and the stationary housing play an important role in centrifugal pumps. Therefore, understanding the influence of the blade number and the leakage flow paths in centrifugal pump is an urgent problem to be solved. In this paper, the vibration and sound radiation of volute under flow excitation was simulated by FEM/BEM acoustic-vibration method. The experiment was carried out to study the effects of blade number on the vibration and noise based on a centrifugal pump with a single entry and a single volute. Comparing the different performances of centrifugal pump with various blade numbers, it was found that with the increase of blade number, the head and shaft power increased gradually, and the efficiency increased first, then decreased and increased with the increase of blade number. In addition, the numerical simulation results of volute with and without leakage flow paths were compared. The vibration and noise induced by inner flow of the pump with different blade number were analyzed under design flow condition. It was found that the results of simulation were validated by the vibration acceleration of the monitoring points on volute compared with the experimental vibration acceleration. The numerical simulation method proposed in this paper could be used to predict flow-induced vibration and acoustic radiation of volutes under design conditions. The errors value of head, efficiency and shaft power between numerical calculation and experiments were within 5.06%, 5.34% and 5.68% respectively. The amplitudes of simulation with the leakage flow paths were coincident with the experimental results than the results without the leakage. The peak error between the simulation amplitude with and without leakage flow paths was 13.5%. To reveal the effects of the blade number on pressure fluctuation and vibration, the contrast with different blade numbers was considered objectively. As the number of blades decreased, the pressure fluctuation and vibration displacement of the volute of centrifugal pump increased. High amplitude regions appeared at the volute tongue, the first and second hydraulic profile of the volute and the eighth hydraulic profile were close to the diffuser. The maximum vibration displacement mainly concentrated at the eighth hydraulic profile. According to the analysis, the significant high levels of vibration velocity can mainly classify in three regions, around the tongue, between the fourth and the sixth hydraulic profile of the volute, and the eighth hydraulic profile was close to the diffuser. However, the variation of the velocity disagreed with the displacement. That meant the vibration velocity was not only relative to the displacement, but also relative to the frequency. In terms of the noise on these impeller with diverse blade number, the vibration speed and radiated sound pressure level of the volute surface first increased and then decreased with the increase of the number of blades, besides, when the impeller was five blades, the vibration speed and noise reached the maximum value. The region of high noise level mainly appears in the vertical direction. The results can provide a reference for the further analysis on vibration and noise reduction design of centrifugal pump.