In this work, we explore the influence of the surface curvature on the contact angle in electrowetting (EW). By using the method of energy minimization, an extended EW equation for EW on curved surfaces is obtained. A curvature-modified EW number is introduced to describe the surface curvature effect. It is found that the variation of the contact angle will be curvature dependent; especially, with decreasing of the system size, the surface curvature effect would be even more significant. Comparing with the planar situation, the contact angle variation decreases on convex surfaces but increases on concave surfaces. Then considering the line tension effect, an extended expression for EW on curved surfaces is proposed. Since curved surfaces are more common, both natural and synthetic, our findings will have important implications for the miniaturization of future electronic products.