Present paper studies the contribution of both the quantum effect and the dust size distribution effect on the shock wave characters. It is concluded that the quantum effect of dust particles is negligible, while the quantum effects of both electrons and ions on the shock wave of a quantum dusty plasma cannot be neglected in certain cases. It is found that the speed and the amplitude of the shock wave, considering the dust size distribution, are larger than that of the quantum dusty plasma with the average dust size of a monosized dust plasma. Furthermore, the speed and the amplitude of the shock wave increase, while the width of the shock wave decreases as the ratios of the maximum dust size to the minimum one increases. The quantum effects may affect both the amplitude and width of the shock wave, while it has no effect on the shock wave speed. The width of the shock wave increases,while its amplitude decreases as $H_e$ and $H_i$ increase.