Both observations and numerical simulations with bin microphysics indicated that aerosol concentrations and size distributions play an important role in cloud droplet spectrum evolution and precipitation formation. With limited prognostic variables, current bulk microphysics parameterization cannot simulate the cloud droplet spectrum evolution properly because of the abnormal broadening problem during condensation. No studies of the effect of the size distribution of aerosols on cloud droplet spectra with bulk scheme simulations have been conducted. The newly developed triple-moment bulk scheme includes an additional spectrum shape parameter and overcomes the abnormal broadening problem, which can be better applied to simulate the main characteristics of cloud droplet spectrum evolution than double-moment schemes. To analyze the effect of the size distribution of aerosols on the cloud droplet spectrum evolution using triple-moment microphysical bulk scheme IAP-LACS which has been developed by Key Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS) of Insitute of Atmospheric Physics (IAP). This work focuses on the effects of three parameters of the size distribution of aerosols (i.e., number concentration, geometric radius, and standard deviation) on the cloud droplet spectrum evolution using WRF-LES ideal simulations. The results of the numerical sensitivity tests for the three parameters show that the newly developed triple-moment water vapor growth scheme coupled with the explicit aerosol activation process is a powerful tool to simulate the effect of the size distribution of aerosols on the cloud droplet spectrum evolution. Aerosol number concentration significantly affects the shape of the cloud droplet spectrum. A high aerosol number concentration results in a narrow droplet spectrum with activated droplets and small average size. By contrast, a low aerosol number concentration produces less droplets but with large radius. Enlarging the geometric radius, which means moving the aerosol spectrum toward a large particle size, leads to cloud droplets with a large size. Notably, the standard deviation plays a less important role in the cloud droplet spectrum than the aerosol number concentration and geometric radius.