Nanowires have unique optical properties and are considered as important building blocks for energy harvesting applications such as solar cells. However, due to their large surface-to-volume ratios, the recombination of charge carriers through surface states reduces the carrier diffusion lengths in nanowires a few orders of magnitude, often resulting in the low efficiency (a few percent or less) of nanowire-based solar cells. Reducing the recombination by surface passivation is crucial for the realization of high-performance nanosized optoelectronic devices but remains largely unexplored. Here we show that a thin layer of amorphous silicon (a-Si) coated on a single-crystalline silicon nanowire, forming a core-shell structure in situ in the vapor-liquid-solid process, reduces the surface recombination nearly 2 orders of magnitude. Under illumination of modulated light, we measure a greater than 90-fold improvement in the photosensitivity of individual core-shell nanowires, compared to regular nanowires without shell. Simulations of the optical absorption of the nanowires indicate that the strong absorption of the a-Si shell contributes to this effect, but we conclude that the effect is mainly due to the enhanced carrier lifetime by surface passivation.