Open MRI systems usually use vertical-field magnets because interventional studies can be performed more conveniently with them. In this paper, we have designed convex-surface gradient coils for a vertical-field open MRI system. To obtain stronger gradient field strength with a smaller coil inductance while maintaining enough space for interventional operations, we have designed gradient coils on convex, rather than planar, surfaces. The convex-surface gradient coils are designed using the finite element method where the convex surfaces are defined at the prolate spheroidal coordinate. We present evaluation results of the convex-surface gradient coils designed with various rates of convexity.