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Recent studies showed that the contact angles of fluids on the carbon nanotubes depend on the nanotubes' curvature. However, the trends of the curvature effect were contradictory, and underline physics has not been fully revealed. This work presents for the first time a molecular perspective of curvature effect on the contact angles. We develop an analytic theory without fitting parameters based on the Young-Dupré equation to provide a fundamental understanding of the intrinsic nature of the curvature effect, which is validated quantitatively by molecular dynamics simulations on water droplets in contact with carbon nanotubes. We find that the contact angle decreases on a concaved substrate and vice versa. A curved hydrophilic surface demonstrates a more significant influence. Additionally, the curvature effect's length scale is governed by the atomic interaction range between liquid and solid. We anticipate that the new understanding of the nanoscale wetting gives new insight into the design of nano-flow systems and the stable superhydrophobic surfaces.