Engineering surfaces that can accelerate droplet detachment are of great importance to a wide range of practical applications, including dropwise condensation, anti-icing, and self-cleaning. Considering the pragmatic effect of reducing contact time (τc), the cylindrical surface is one of the most popular passive approaches for achieving this purpose. Owing to the absence of a suitable way for the experimental observation, we use molecular dynamics (MD) simulations to obtain an in-depth understanding of droplet impingement on the curved surface at the molecular level together with the contact time variation. Accordingly, the regimes of τc upon curved surfaces are well recognized by summarizing the τc variation, which are stable reducing τc regime and hybrid τc regime. We propose a law of τc ∝ α-0.226 to predict the τc variation in the stable reducing τc regime. And for the hybrid τc regime, the τc variation is specifically defined as three parts, including the delayed τc, limited τc, and transitional τc regions. Moreover, we investigate the effect of the dimensionless length of curved surfaces on the τc variation in detail. This work paves the way to design a more effective curved surface to promote the nanodroplet rebound.