Polycarbonate (PC) with high transmittance, stable mechanical performance and environmental resistance is crucial for practical applications. In this work, we report a method for the preparation of a robust antireflective (AR) coating by a simple dip-coating process of a mixed ethanol suspension consisting of tetraethoxysilane (TEOS) base-catalyzed silica nanoparticles (SNs) and acid-catalyzed silica sol (ACSS). ACSS greatly improved the adhesion and durability of the coating, and the AR coating exhibited high transmittance and mechanical stability. Water and hexamethyldisilazane (HMDS) vapor treatment were further employed to improve the hydrophobicity of the AR coating. The as-prepared coating exhibited excellent antireflective properties, with an average transmittance of 96.06% in the wavelength range of 400 to 1000 nm, which is 7.55% higher than the bare PC substrate. After sand and water droplet impact tests, the AR coating still maintained enhanced transmittance and hydrophobicity. Our method shows a potential application for the preparation of hydrophobic AR coatings on a PC substrate.