The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $〈\ensuremath{\delta}{N}_{0}^{2}〉\ensuremath{\sim}{N}^{22/15}$ and the fluctuations vanish when temperature approaches the BEC critical temperature.